Almost any kind of horse can be a show jumper. But the best show jumping horses are called warmblooded or thouroughbreds breeds. They are good show jumpers because they are tall. Usually about 16 hands tall. That's how you measure a horse. In hands.
Warmblooded horses are a medium size horses that were bred in EUROPE originally.
Thoroughbred horses are race horses and are called " hotblooded" because they are fast, agile and spirit.