I'm going to throw in my unsolicited opinion... While fine as a "last resort" I think it is a bad idea to count on a pistol as a self-defense weapon while mounted. There are simply too many things that can go wrong.
I am involved in mounted shooting. I see many horses do fine and excel at it. There is a big difference between this and a hostile encounter.
Mounted shooting is running a prescribed course in a controlled environment. The targets are inanimate and do not move. Both rider and horse know exactly what to expect when they enter the ring. The horse usually hears several gunshots before he enters the ring. Once the "go" signal is given, both rider and horse charge towards a balloon and know that a gunshot is coming. Finally, the blanks used for mounted shooting have no recoil.
If you are in a life threatening situation, adrenaline is bound to be running high. It is probably difficult enough to deal with things, no less draw a gun, make the decision to fire on another person and then hit your target. Then of course, there are all the legal ramifications involved when you brandish, threaten, shoot at, hit or kill someone with a gun.
Out on trail, you are in an environment that even a trained shooting horse would not expect to hear a gunshot. If you are in a life-threatening encounter, things will likely be pretty high-strung as it is. You will probably get nervous and the horse will feed off that. Even if you remain calm, the horse will probably be nervous since they tend to sense those things.
So now you are pumped up, the perp is probably moving a bit (maybe to get out of the way of your horse who isn't staying still). You draw your gun and fire. BOOM! Already nervous horse dumps you. You drop the gun. Your shot missed, the perp has your gun and you are injured on the ground.
Let's say the horse didn't spook from the unexpected shot and you stayed on. Instead you shot high, missed and hit someone else.
I do believe that the presence of a firearm is usually enough to ward off any would-be attacker. Predators go for the easy target, not the armed ones. You and your horse may also be able to function in a high-stress dangerous encounter to stop a threat with a well placed shot.
I am merely suggesting to look at the downside. There are much more effective ways (IMO) to practice self-defense on trail than using a gun. Scott Hansen has some great techniques which seem much safer than firing live ammo from horseback.
Good luck and be safe.