Because the Samurai's Kyuujutsu line is based on the Japanese Hankyuu
, which is a longbow used while mounted. A few of those abilities also give a bonus to riding stuff for that exact reason. Also, it is rather tropetastic for western shooters to also have a horse (which is what Silver is from, Silver being the Lone Ranger's horse). Shooting from a horse, or a horse chase-scene is a classic for any western movie or show. In actuality? Horses were really necessary in an area where the climate is really desperate and harsh.