Horses of this breed are used competitively in quarter horse racing, in which races typically take place over distances of a quarter of a mile. This is where the breed got its name from. These horses are also used to perform in rodeos and to work on ranches.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.