There isn't really a "Best Horse" in the game- The horses all have strengths and weaknesses. You might prefer high speed over high health, someone else might prefer high health or high stamina.
You need to consider both the class of the horse and the stats. Generally speaking, if you want a fast horse, then look for a race class horse. If you want a fearless horse with high health go for a war horse. For a good all-rounder, look for a multi-class (eg Race/war or race/work).
Keep in mind also that it appears that the temperament/bravery of the horses seems to be completely random - as several people have found that horses of the same breed (bonded in the same way) can perform differently in terms of bravery. So no one breed seems to be any better/worse than others at bravery (Although Arabians are usually always skittish, war horses are usually very brave)
To help you choose horses based on their stats, I've listed the top level horses in each stat category, and then below that a list of all horses and their stats.
Top Stat Horses
This lists the horses (colour variant for each breed) that has the highest stat in the following categories. Eg you could say these were the "best" horses in each category.
I've included the class because another consideration is how well they perform in battle/hunting. So if you are comparing horses, a "War" horse will generally be braver than a "Race" horse.
Top Health (7)
Andalusian (War) - Rose Grey
Arabian (Race) - Rose Grey Bay
Ardennes (War) - Iron Grey Roan / Strawberry Roan
Kladruber (Race/War) - Dapple Rose Grey, Silver
Mustang (Work/War) - Black Overo, Buckskin, Chestnut Tovero, Red Dun Overo
Turkoman (Race/War) - Black, Chestnut, Dark Bay, Gold, Grey, Perlino, Silver
Top Speed (7)
Criollo (Race/War) - Bay Frame Overo, Marble Sabino
Gypsy Cob - Splashed Bay / Splashed Piebald
Missouri Fox Trotter (Race/Work) - Amber, Black Tovero, Brindle, Silver Dapple
Mustang (Work/War) - Black Overo, Buckskin, Chestnut Tovero, Red Dun Overo
Nokota (Race) - Reverse Dapple Roan
Norfolk Roadster (Race/War) - Dappled Buckskin & Spotted Tricolour
Thoroughbred (Race) - Black Chestnut, Brindle, Dapple Black
Top Stamina (7)
Arabian (Race) - Rose Grey Bay
Breton (Race/War) - Mealey Dapple, Steel Grey
Kladruber (Race/War) - Dapple Rose Grey, Silver
Top Acceleration (6)
Arabian (Race) - Black / Rose Grey Bay / White
Gypsy Cob - Splashed Bay / Splashed Piebald
Norfolk Roadster (Race/War) - Dappled Buckskin & Spotted Tricolour
Summary - "Best" Horses (Best combination of Health/Stamina/Speed/Bravery)
Online
Level 20 Role horses - Breton/Gypsy Cob/Kladruber/Norfolk Roadster. Missouri Fox Trotter (All colours). Mustang (Black Overo/Buckskin/Chestnut Tovero/Red Dun Overo). Turkoman (All colours). Arabians (Rose Bay) have the health/speed/Stamina but I personally find them too skittish, but if that doesn't bother you then they are a top pick.
Storymode
Free horses - White Arabian (Found at Lake Isabella). Dapple grey Hungarian (Steal from Mr. Wroble's barn during the "Money Lending and other Sins" mission, or from Benedict Allbright in the "Good, Honest, Snake Oil" bounty hunting mission in Valentine (just jump on his horse to chase him, instead of your own). It is possible to get the silver dapple Missouri Fox Trotter for free early in the game - There is an NPC encounter around Moonstone pond that can glitch and spawn it alive (it's supposed to be dead). I've seen it suggested you need to get there just before 6am (which worked for me) This video explains it (although it says the time is just before 7am).
To buy - Gold Turkoman (After Chapter 4) or Chocolate Roan Dutch Warmblood (Chapter 2 - After unlocking Valentine Stables). Better horses become available after the Epilogue.
Stats
Health
7
Andalusian - Rose Grey
Arabian - Rose Grey Bay
Ardennes - Iron Grey Roan, Strawberry Roan
Kladruber - Dapple Rose Grey, Silver
Mustang - Black Overo, Buckskin, Chestnut Tovero, Red Dun Overo
Turkoman - Black, Chestnut, Dark Bay, Gold, Grey, Perlino, Silver
6
Arabian - Black
Breton - Mealey Dapple, Steel Grey
Dutch Warmblood - "Buell"
Kladruber - Cremello, Grey
5
American Paint - Grey Overo
Andalusian - Dark Bay
Appaloosa - Brown Leopard, Leopard
Arabian - White
Ardennes - Bay Roan
Breton - Grullo Dun, Seal Brown
Criollo - Bay Frame Overo, Marble Sabino
Dutch Warmblood - Chocolate Roan
Gypsy Cob - Splashed Bay, Splashed Piebald
Hungarian Halfbred - Dapple Dark Grey
Kladruber - Black, White
Missouri Fox Trotter - Amber Champagne, Black Tovero, Blue Roan, Buckskin Brindle, Dapple Grey, Silver Dapple Pinto
Mustang - Tiger Striped Bay
4
American Standardbred - Silver Tail Buckskin
Breton - Red Roan, Sorrel
Criollo - Bay Brindle, Sorrel Overo
Dutch Warmblood - Chocolate Roan, Seal Brown, Sooty Buckskin
Hungarian Halfbred - Flaxen Chestnut, Piebald Tobiano
Gypsy Cob - Palomino Blagdon, Skewbald
Mustang - Grullo Dun, Wild Bay
Norfolk Roadster - Dappled Buckskin & Spotted Tricolour
Shire - Dark Bay, Light Grey, Raven Black
Tennessee Walker - Flaxen Roan
Thoroughbred - "Rachel"
3
American Paint - Overo, Tobiano, Splashed White
American Standardbred - Black, Buckskin, Palomino Dapple
Appaloosa - Blanket, Leopard Blanket
Belgian Draft - Chestnut, Mealy Chestnut
Criollo - Blue Roan Overo, Dun
Gypsy Cob - Piebald, White Blagdon
Kentucky Saddler - Black, Chestnut Pinto, Grey, Silver Bay
Nokota - Blue Roan, Reverse Dapple Roan, White Roan
Norfolk Roadster - Piebald Roan & Rose Grey
Suffolk Punch - Red Chestnut, Sorrel
Tennessee Walker - Black Rabicano, Chestnut, Dapple Bay, Gold Palomino, Mahogany Bay, Red Roan
Thoroughbred - Black Chestnut, Blood Bay, Brindle, Dapple Black, Dapple Grey
2
Morgan - Bay, Bay Roan, Flaxen Chestnut, Liver Chestnut, Palomino
Norfolk Roadster - Black, Speckled Grey
Stamina
7
Arabian - Rose Grey Bay
Breton - Mealey Dapple, Steel Grey
Kladruber - Dapple Rose Grey, Silver
Mustang - Black Overo, Buckskin, Chestnut Tovero, Red Dun Overo
6
Appaloosa - Brown Leopard, Leopard
Arabian - Black
Breton - Grullo Dun, Seal Brown
Criollo - Bay Frame Overo, Marble Sabino
Dutch Warmblood - "Buell", Chocolate Roan
Gypsy Cob - Splashed Bay, Splashed Piebald
Kladruber - Cremello, Grey
Missouri Fox Trotter - Amber Champagne, Black Tovero, Blue Roan, Buckskin Brindle, Dapple Grey, Silver Dapple Pinto
Norfolk Roadster - Dappled Buckskin, Spotted Tricolour
5
American Paint - Grey Overo, Splashed White
Andalusian - Rose Grey
Ardennes - Iron Grey Roan, Strawberry Roan
Arabian - White
Breton - Red Roan, Sorrel
Criollo - Bay Brindle, Sorrel Overo
Dutch Warmblood - Chocolate Roan, Seal Brown, Sooty Buckskin
Gypsy Cob - Palomino Blagdon, Skewbald
Kladruber - Black, White
Mustang - Tiger Striped Bay
Norfolk Roadster - Piebald Roan & Rose Grey
Tennessee Walker - Flaxen Roan
Turkoman - Black, Chestnut, Dark Bay, Gold, Grey, Perlino, Silver
4
American Paint - Overo, Tobiano
American Standardbred - Silver Tail Buckskin
Andalusian - Dark Bay
Appaloosa - Blanket, Leopard Blanket
Ardennes - Bay Roan
Criollo - Blue Roan Overo, Dun
Gypsy Cob - Piebald, White Blagdon
Hungarian Halfbred - Dapple Dark Grey
Morgan - Liver Chestnut
Mustang - Grullo Dun, Wild Bay
Norfolk Roadster - Black, Speckled Grey
Shire - Raven Black
Suffolk Punch - Red Chestnut, Sorrel
Tennessee Walker - Gold Palomino, Mahogany Bay
Thoroughbred - "Rachel"
3
American Standardbred - Black, Buckskin, Palomino Dapple
Belgian Draft - Chestnut, Mealy Chestnut
Hungarian Halfbred - Flaxen Chestnut, Piebald Tobiano
Morgan - Bay, Bay Roan, Flaxen Chestnut, Palomino
Nokota - Blue Roan, Reverse Dapple Roan, White Roan
Shire - Dark Bay, Light Grey
Tennessee Walker - Black Rabicano, Chestnut, Dapple Bay, Red Roan
Thoroughbred - Black Chestnut, Blood Bay, Brindle, Dapple Black, Dapple Grey
2
Kentucky Saddler - Black, Chestnut Pinto, Grey, Silver Bay
Speed
7
Criollo - Bay Frame Overo, Marble Sabino
Gypsy Cob - Splashed Bay, Splashed Piebald
Missouri Fox Trotter - Amber Champagne, Black Tovero, Blue Roan, Buckskin Brindle, Dapple Grey, Silver Dapple Pinto
Nokota - Reverse Dapple Roan
Norfolk Roadster - Dappled Buckskin, Spotted Tricolour
Thoroughbred - Black Chestnut, Brindle, Dapple Black
6
Arabian - Black, Rose Grey Bay, White
Breton - Mealey Dapple, Steel Grey
Criollo - Bay Brindle, Sorrel Overo
Mustang - Black Overo, Buckskin, Chestnut Tovero, Red Dun Overo
Norfolk Roadster - Piebald Roan, Rose Grey
Thoroughbred - "Rachel"
Turkoman - Black, Chestnut, Dark Bay, Gold, Grey, Perlino, Silver
5
American Standardbred - Palomino Dapple, Silver Tail Buckskin
Breton - Grullo Dun, Seal Brown
Criollo - Blue Roan Overo, Dun
Dutch Warmblood - "Buell"
Gypsy Cob - Palomino Blagdon, Skewbald
Norfolk Roadster - Black, Speckled Grey
4
American Paint - Grey Overo
American Standardbred - Black, Buckskin
Appaloosa - Brown Leopard, Leopard
Breton - Red Roan, Sorrel
Dutch Warmblood - Chocolate Roan
Gypsy Cob - Piebald, White Blagdon
Kladruber - Dapple Rose Grey, Silver
Morgan - Liver Chestnut
Mustang - Tiger Striped Bay
Nokota - Blue Roan, White Roan
Thoroughbred - Blood Bay, Dapple Grey
3
American Paint - Overo, Tobiano, Splashed White
Andalusian - Dark Bay, Rose Grey
Appaloosa - Blanket, Leopard Blanket
Ardennes - Bay Roan, Iron Grey Roan, Strawberry Roan
Belgian Draft - Chestnut, Mealy Chestnut
Dutch Warmblood - Chocolate Roan, Seal Brown, Sooty Buckskin
Hungarian Halfbred - Dapple Dark Grey, Flaxen Chestnut, Piebald Tobiano
Kentucky Saddler - Black, Chestnut Pinto, Grey, Silver Bay
Kladruber - Cremello, Grey
Morgan - Bay, Bay Roan, Flaxen Chestnut, Palomino
Mustang - Grullo Dun, Wild Bay
Shire - Dark Bay, Light Grey, Raven Black
Suffolk Punch - Red Chestnut, Sorrel
Tennessee Walker - Gold Palomino, Flaxen Roan
2
Kladruber - Black, White
Tennessee Walker - Black Rabicano, Chestnut, Dapple Bay, Mahogany Bay, Red Roan
Acceleration
6
Arabian - Black, Rose Grey Bay, White
Gypsy Cob - Splashed Bay, Splashed Piebald
Norfolk Roadster - Dappled Buckskin, Spotted Tricolour
5
Criollo - Bay Frame Overo, Marble Sabino
Dutch Warmblood - "Buell"
Gypsy Cob - Palomino Blagdon, Skewbald
Kladruber - Dapple Rose Grey, Silver
Missouri Fox Trotter - Amber Champagne, Black Tovero, Blue Roan, Buckskin Brindle, Dapple Grey, Silver Dapple Pinto
Nokota - Reverse Dapple Roan
Norfolk Roadster - Piebald Roan & Rose Grey
Thoroughbred - Black Chestnut, Brindle, Dapple Black
Turkoman - Black, Chestnut, Dark Bay, Gold, Grey, Perlino, Silver
4
American Paint - Grey Overo
American Standardbred - Palomino Dapple, Silver Tail Buckskin
Breton - Mealey Dapple, Steel Grey
Criollo - Bay Brindle, Sorrel Overo
Gypsy Cob - Piebald, White Blagdon
Kladruber - Cremello, Grey
Mustang - Black Overo, Buckskin, Chestnut Tovero, Red Dun Overo
Norfolk Roadster - Black, Speckled Grey
Thoroughbred - "Rachel"
3
American Paint - Overo, Tobiano, Splashed White
American Standardbred - Black, Buckskin
Andalusian - Dark Bay, Rose Grey
Appaloosa - Brown Leopard, Blanket, Leopard Blanket, Leopard
Ardennes - Bay Roan, Iron Grey Roan, Strawberry Roan
Belgian Draft - Chestnut, Mealy Chestnut
Breton - Grullo Dun, Seal Brown
Criollo - Blue Roan Overo, Dun
Dutch Warmblood - Chocolate Roan, Seal Brown, Sooty Buckskin
Hungarian Halfbred - Dapple Dark Grey, Flaxen Chestnut, Piebald Tobiano
Kentucky Saddler - Black, Chestnut Pinto, Grey, Silver Bay
Kladruber - Black, White
Mustang - Grullo Dun, Tiger Striped Bay, Wild Bay
Nokota - Blue Roan, White Roan
Tennessee Walker - Flaxen Roan
Thoroughbred - Blood Bay, Dapple Grey
2
Breton - Red Roan, Sorrel
Morgan - Bay, Bay Roan, Flaxen Chestnut, Liver Chestnut, Palomino
Shire - Dark Bay, Light Grey, Raven Black
Suffolk Punch - Red Chestnut, Sorrel
Tennessee Walker - Black Rabicano, Chestnut, Dapple Bay, Gold Palomino, Mahogany Bay, Red Roan
My Suggested Horse Rankings
By Stats (as best as I could!)
Not sure what to call this.... but to help you choose horses based on their stats, I've tried to rank the horses here in order of their stats. Where a horse is lower in one stat and higher in another, I've tried to rank them based on what I think people would place higher importance on (speed/stamina being slightly more important than health, with acceleration least important). But the stats are all included so you can make your own decision.
Arabian - Rose Grey Bay
(Health 7 | Stamina 7 | Speed 6 | Acceleration 6) - Type: Superior. Handling: Elite
Mustang - Black Overo, Buckskin, Chestnut Tovero, Red Dun Overo
(Health 7 | Stamina 7 | Speed 6 | Acceleration 4) - Type: War/Work. Handling: Standard
Gypsy Cob - Splashed Piebald, Splashed Bay
(Health 5 | Stamina 6 | Speed 7 | Acceleration 6) - Type: Multi. Handling: Standard
Missouri Fox Trotter - Amber Champagne, Black Tovero, Blue Roan, Buckskin Brindle, Dapple Grey, Silver Dapple Pinto
(Health 5 | Stamina 6 | Speed 7 | Acceleration 5) - Type: Race/Work. Handling: Standard
Turkoman - Black, Chestnut, Dark Bay, Gold, Grey, Perlino, Silver
(Health 7 | Stamina 5 | Speed 6 | Acceleration 5) - Type: Race/War. Handling: Standard
Breton - Mealey Dapple, Steel Grey
(Health 6 | Stamina 7 | Speed 6 | Acceleration 4) - Type: Race/War. Handling: Standard
Norfolk Roadster - Dappled Buckskin & Spotted Tricolour
(Health 4 | Stamina 6 | Speed 7 | Acceleration 6) - Type: Race/War. Handling: Standard
Kladruber - Dapple Rose Grey, Silver
(Health 7 | Stamina 7 | Speed 4 | Acceleration 5) - Type: Race/War. Handling: Standard
Arabian - Black
(Health 6 | Stamina 6 | Speed 6 | Acceleration 6) - Type: Superior. Handling: Elite
Dutch Warmblood - "Buell"
(Health 6 | Stamina 6 | Speed 5 | Acceleration 5) - Type: Work. Handling: Standard
Arabian - White
(Health 5 | Stamina 5 | Speed 6 | Acceleration 6) - Type: Superior. Handling: Elite
Gypsy Cob - Palomino Blagdon, Skewbald
(Health 4 | Stamina 5 | Speed 5 | Acceleration 5) - Type: Multi. Handling: Standard
Andalusian - Rose Grey
(Health 7 | Stamina 5 | Speed 3 | Acceleration 3) - Type: War. Handling: Standard
Criollo - Bay Frame Overo, Marble Sabino
(Health 5 | Stamina 6 | Speed 7 | Acceleration 5) - Type: Race/War. Handling: Standard
Kladruber - Cremello, Grey
(Health 6 | Stamina 6 | Speed 3 | Acceleration 4) - Type: Race/War. Handling: Standard
Ardennes - Iron Grey Roan / Strawberry Roan
(Health 7 | Stamina 5 | Speed 3 | Acceleration 3) - Type: War. Handling: Standard
Breton - Grullo Dun, Seal Brown
(Health 5 | Stamina 6 | Speed 5 | Acceleration 3) - Type: Race/War. Handling: Standard
American Paint - Grey Overo
(Health 5 | Stamina 5 | Speed 4 | Acceleration 4) - Type: Work. Handling: Standard
Appaloosa - Brown Leopard / Leopard
(Health 5 | Stamina 6 | Speed 4 | Acceleration 3) - Type: Work. Handling: Standard
Dutch Warmblood - Chocolate Roan
(Health 5 | Stamina 6 | Speed 4 | Acceleration 3) - Type: Work. Handling: Standard
Mustang - Tiger Striped Bay
(Health 5 | Stamina 5 | Speed 4 | Acceleration 3) - Type: War/Work. Handling: Standard
Gypsy Cob - Piebald, White Blagdon
(Health 3 | Stamina 4 | Speed 4 | Acceleration 4) - Type: Multi. Handling: Standard
Andalusian - Dark Bay
(Health 5 | Stamina 4 | Speed 3 | Acceleration 3) - Type: War. Handling: Standard
Ardennes - Bay Roan
(Health 5 | Stamina 4 | Speed 3 | Acceleration 3) - Type: War. Handling: Standard
Hungarian Halfbred - Dapple Dark Grey
(Health 5 | Stamina 4 | Speed 3 | Acceleration 3) - Type: War. Handling: Standard
American Standardbred - Silver Tail Buckskin
(Health 4 | Stamina 4 | Speed 5 | Acceleration 4) - Type: Race. Handling: Race
Kladruber - Black, White
(Health 5 | Stamina 5 | Speed 2 | Acceleration 3) - Type: Race/War. Handling: Standard
Criollo - Bay Brindle, Sorrel Overo
(Health 4 | Stamina 5 | Speed 6 | Acceleration 4) - Type: Race/War. Handling: Standard
Thoroughbred - "Rachel"
(Health 4 | Stamina 4 | Speed 6 | Acceleration 4) - Type: Race. Handling: Race
Breton - Red Roan, Sorrel
(Health 4 | Stamina 5 | Speed 4 | Acceleration 2) - Type: Race/War. Handling: Standard
Dutch Warmblood - Chocolate Roan, Seal Brown, Sooty Buckskin
(Health 4 | Stamina 5 | Speed 3 | Acceleration 3) - Type: Work. Handling: Standard
Tennessee Walker - Flaxen Roan
(Health 4 | Stamina 5 | Speed 3 | Acceleration 3) - Type: Riding. Handling: Standard
Mustang - Grullo Dun, Wild Bay
(Health 4 | Stamina 4 | Speed 3 | Acceleration 3) - Type: War/Work. Handling: Standard
Norfolk Roadster - Piebald Roan & Rose Grey
(Health 3 | Stamina 5 | Speed 6 | Acceleration 5) - Type: Race/War. Handling: Standard
Nokota - Reverse Dapple Roan
(Health 3 | Stamina 3 | Speed 7 | Acceleration 5) - Type: Race. Handling: Race
Thoroughbred - Black Chestnut, Brindle, Dapple Black (Special edition)
(Health 3 | Stamina 3 | Speed 7 | Acceleration 5) - Type: Race. Handling: Race
Arabian - Warped Brindle
(Health 3 | Stamina 5 | Speed 6 | Acceleration 4) - Type: Superior. Handling: Elite
Arabian - Red Chestnut
(Health 3 | Stamina 4 | Speed 5 | Acceleration 4) - Type: Superior. Handling: Elite
American Paint - Splashed White
(Health 3 | Stamina 5 | Speed 3 | Acceleration 3) - Type: War. Handling: Standard
Shire - Raven Black
(Health 4 | Stamina 4 | Speed 3 | Acceleration 2) - Type: Draft. Handling: Heavy
Hungarian Halfbred - Flaxen Chestnut, Piebald Tobiano
(Health 4 | Stamina 3 | Speed 3 | Acceleration 3) - Type: War. Handling: Standard
American Paint - Overo, Tobiano
(Health 3 | Stamina 4 | Speed 3 | Acceleration 3) - Type: Work. Handling: Standard
American Standardbred - Palomino Dapple
(Health 3 | Stamina 3 | Speed 5 | Acceleration 4) - Type: Race. Handling: Race
Norfolk Roadster - Black, Speckled Grey
(Health 3 | Stamina 4 | Speed 5 | Acceleration 4) - Type: Race/War. Handling: Standard
Appaloosa - Few Spot
(Health 3 | Stamina 5 | Speed 3 | Acceleration 3) - Type: Work. Handling: Standard
Appaloosa - Blanket, Leopard Blanket
(Health 3 | Stamina 4 | Speed 3 | Acceleration 3) - Type: Work. Handling: Standard
American Standardbred - Black, Buckskin
(Health 3 | Stamina 3 | Speed 4 | Acceleration 3) - Type: Race. Handling: Race
Criollo - Blue Roan Overo, Dun
(Health 3 | Stamina 4 | Speed 5 | Acceleration 3) - Type: Race/War. Handling: Standard
Nokota - Blue Roan, White Roan
(Health 3 | Stamina 3 | Speed 4 | Acceleration 3) - Type: Race. Handling: Race
Thoroughbred - Blood Bay, Dapple Grey
(Health 3 | Stamina 3 | Speed 4 | Acceleration 3) - Type: Race. Handling: Race
Shire - Dark Bay, Light Grey,
(Health 4 | Stamina 3 | Speed 3 | Acceleration 2) - Type: Draft. Handling: Heavy
Suffolk Punch - Red Chestnut, Sorrel
(Health 3 | Stamina 4 | Speed 3 | Acceleration 2) - Type: Draft. Handling: Heavy
Kentucky Saddler - Buttermilk Buckskin
(Health 3 | Stamina 3 | Speed 4 | Acceleration 2) - Type: Riding. Handling: Standard
Tennessee Walker - Gold Palomino
(Health 3 | Stamina 4 | Speed 3 | Acceleration 2) - Type: Riding. Handling: Standard
Belgian Draft - Chestnut, Mealy Chestnut
(Health 3 | Stamina 3 | Speed 3 | Acceleration 3) - Type: Draft. Handling: Heavy
Morgan - Liver Chestnut
(Health 2 | Stamina 4 | Speed 4 | Acceleration 2) - Type: Riding. Handling: Standard
Tennessee Walker - Mahogany Bay
(Health 3 | Stamina 4 | Speed 2 | Acceleration 2) - Type: Riding. Handling: Standard
Kentucky Saddler - Black, Chestnut Pinto, Grey, Silver Bay
(Health 3 | Stamina 2 | Speed 3 | Acceleration 3) - Type: Riding. Handling: Standard
Morgan - Bay, Bay Roan, Flaxen Chestnut, Palomino
(Health 2 | Stamina 3 | Speed 3 | Acceleration 2) - Type: Riding. Handling: Standard
Tennessee Walker - Black Rabicano, Chestnut, Dapple Bay, Red Roan
(Health 3 | Stamina 3 | Speed 2 | Acceleration 2) - Type: Riding. Handling: Standard