Just make sure that whatever gun you decide to carry, that you are familiar with it - so that you can handle it in the dark, that you are comfortable shooting it - if you pick it up you better be prepared to use it, and, that your kids respect the gun - that they never touch it without your permission and supervision. Also, make sure that your horse is somewhat desensitized to "gunshots" (or firecrackers), before you routinely carry it on trail.
A .22 is a small framed gun that had no "kick" to it, while a .38 or better, has some kick, it definitely has more stopping power. Anything larger becomes a burden to carry. They're heavier and bulkier, and what's the point of letting people 9ie "bad guys") know you're carrying a gun. The mileage you get is when the bad guys don't know if you're carrying a gun. If they see that you are carrying a gun, then you'd better be prepared to fight for it. That's a whole other situation. Think before you carry one. They carry more responsibility than you know.
My gun of choice is a Colt 45 Combat Commander - or a Ruger Security Six .357 loaded with 38 rounds (but I have a large hand and long fingers). For carrying about and in the car I have a neat little stainless snub nose 38 - nice little gun that is just big enough to be intimidating.