Pistoleer on horseback shoots an armored man in the head and fails to penetrate, English Civil War, 1643

Well, I'm sure he can still hear his tinnitus, at least

Well, you can shoot a horse, but the issue is that horses are bigger and hardier than people. You'd do a bit of harm, but not necessarily kill it, and even if you did serious damage, a man with a dying horse is much more dangerous than a horse with a dying man, you know?