Do race horses have to be purebred?

No. The Mustang has just about every breed of horse bred in its gene pool, from the Spanish Barbarians to Thoroughbreds, Quarter Horses, Arabians, Clydesdales, or even Andalusian. The Mustang is known as its own breed like the Arabian or the Halter Reel, but it is most commonly known as mesteña, which is Spanish for wild or stray, since Mustangs are made up of horses that have escaped or ran away from their human owners.