The main forms of horse racing which most people bet on feature Thoroughbred horses. There are, however, several other breeds of horses involved in horse racing for sport. There are Arabian horses, Standardbreds and American Quarter Horses for example.These feature in other forms of horse racing such as harness racing, endurance riding and quarter horse racing.lthough there are plenty of races for other breeds, the biggest races in the world are open only to Thoroughbred horses. Horses of this breed are known for their strength, speed and athleticism, and they are also used for other equestrian sports as well as racing.