The way I've always gun trained a horse is to start with a 22. I stand on the ground with the horse in hand and choose an area where it will not damage the gun if I need to drop it - I always give the horse a warning before shooting - I use "pass auf" which is German for "pay attention" (I'm not gun shy but if someone shoots a few feet away from me without warning I'll jump, too!). I extend the gun away from me so I have more room to drop it if the horse really spooks (I've never had to drop the gun, but you want to be safe if you have to - you do not want it in your hand if you need both hands to keep hold of the horse!) - also, I've found that the 22's with longer barrels are quieter and don't spook the horse as much.
Generally the horse does okay and I repeat that for a short time everyday until the horse does not move when I fire.
I then mount the horse and do the same thing over again - making certain I hold the gun extended to the side in case I need to drop it and staying on a relatively soft surface for the same reason. I repeat this for a short time every day until the horse does not move when I shoot (what mine do is they tense a little in preparation when I say "pass auf" but don't move otherwise).
Once they seem pretty secure with the 22 I will start all over from the ground with a larger, noisier gun. They generally learn the newer gun very quickly.
I use the ground method to train my dogs as well and it seems to work fine.
I also agree it's a good idea to carry the gun on your person when possible - I used to carry it on my saddle because of the weight but was seperated from my horse one year in a bad fall and missed the gun and my water bottle (as well as the horse, of course!!).
Good luck!
Mary M.