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Equus: The Evolution Of The Horse (YouTube Video)
Abyssinian
Akhal-Teke
Albanian
Altai *
American Albino
American Cream Draft
American Gaited Pony
25 American Indian Horse
American Miniature
American Paint
37 American Saddle Horse
American Shetland Pony
American Walking Pony
29. American Warmblood
Andalusian
29. Anglo-Arabian
29. Anglo-Kabarda*
26 Appaloosa
38 AraAppaloosa
26. Arabian
26. Ardennes*
29. Asturian*
29. Australian Brumby*
Australian Pony
39 Australian Stock Horse
40. Azteca

6 k Banker
29. Barb*
Bashkir
Bashkir Curly
38 Belgian
Belgian Warmblood
Black Forest Chestnut
29. Boer*
29. Breton*
Buckskin
29. Budyonny*
29. Byelorussian Harness Horse*

Camargue
29. Campolina*
36. Canadian
25 Canadina Sport Horse
29. Carthusian*
25 Caspian
Cayuse Indian Pony
29. Chilean Corralero*
3 Chincoteage Assateague
40. Cleveland Bay
26. Clydesdale
29. Colorado Ranger Horse*
29. Connemara Pony
43 Criollo
37 Dales Pony
Dartmoor Pony
29. Deliboz*
29. Døle*
9 k Don Horse
39. Donkey
Dulmen
29. Dutch Draft*
26 Dutch Warmblood

29. Egyptian*
29. Eriskay Pony*
Exmoor
36. Falabella
6 k Fell Pony
29. Finnhorse*
29. Fjord Pony
40 Florida Cracker Horse
29. Frederiksborg*
Friesian
29. Galiceño*
29. Galician Pony*
Gelderlander
29. Gidrán*
29. Golden American Saddlebred*
9 k Gotland Pony
Groningen
29. Guangxi*
Gypsy Vanner
29. Hackney Horse
Haflinger
Half Arabian
Hanoverian
29. Hequ*
Highland Pony
29. Hokkaido*
Holsteiner
29. Hungarian Warmblood*
6 k Icelandic Horse
40. Irish Draft
36. Irish Hunter

Knabstruper
Lipizzaner
29. Lusitano
9 k Mérens
29. Missouri Fox Trotter
9 k Morab
Morgan Horse
Moroccan Barb
Mountain Pleasure Horse
Mule
Mustang
National Show Horse
3 National Spotted Saddle Horse
New Forest Pony
26. Noriker
6 k Oldenburg
Paint
Palomino
Paso Fino
Percheron
Peruvian Paso
35. Pintabian
35. Pinto
Poitevin
Pony Of The Americas
Przewalski's Horse
QuArab Horse
Quarter Horse
Racking Horse
Rocky Mountain Horse

Selle Francais
Shagya Arabian
9 k Shetland Pony
Shire Horse
19. Spanish Barb
35. Spanish Mustang
Standardbred
Suffolk Punch
Swedish Ardennes
Swedish Warmblood
9 k Tarpan
6 k Tennessee Walking Horse
35. Thoroughbred
36. Trakehner
Welsh Cob
35. Welsh Pony
Westphalian
35. Wurttemburg
35. Zebra

Some data adapted from the following sources,
Oklahoma State University list of livestock breeds
Kentucky Horse Park