Horses get used to things surprisingly easily. (Kinda like people.) If you train them close to people firing guns, they won't flee from guns. Some horses want

Horses get used to things surprisingly easily. (Kinda like people.) If you train them close to people firing guns, they won't flee from guns. Some horses want to "overthrown" you even in normal circumstances, and almost all of them have a light instinct of getting you out from their backs. But I imagine a large part of forming a cavalry is picking (and breeding and training) the best horses for the role.