We have been training cav horses for over 20 years and have recently gotten into mounted shooting. I have found that using the just the black powder caps are the best (for us) to start with. We start by holding the horse and shooting 20ft away with the caps and move in closer and closer until we are standing right next to them. Then we move the the .22 (we use the blanks from the hardware store that is used to shoot nails in concrete- super cheap). Then we move to a .357 blank. Once the horse stands for that, we mount and start over with the caps- but we have someone on an expericenced horse shoot next to the new horse. We repeat the process mounted and once the horse takes to the neighboring horse being shot off of, we move to shooting caps off of the new horse and progress from there. The last step is using a load in the black powder gun and finally, for the mounted shooting horse, the .45 long colt. Believe me, the difference between the .45 and the cav pistols are very different. We have seasoned cav horses who do not take to the .45's very quickly. And there is the exploding balloon for them to get use to also!
Good luck training your horse. Slow and steady wins the race! And, if you horse will take earplugs and leave them in, use them. It will protect their ears!