Good and valid points, all.
I think back to a woman who died a few years back in Banff(?) or Calgary(?) because of a cougar attack.. Any Alberta/BC peoples may remember this. Details being foggy [for me], she was alone and unarmed from what I remember. Wouldn't that be the worst case scenario?
Buddy system with added defenses are always an asset! Especially if you're in their territory... A gun would be worth it, provided the horse was desensitized to the sound/rider to the punch.. Otherwise, the horse would spook at the gun; and to have the rider to fall with a fire arm is equally dangerous.
I'm sure with time, confidence, knowledge and experience, you'll be good OP.