Is it recommended to only fire a handgun from your horse, of can you also use a rifle?
In the sport of mounted shooting we use single action revolvers (pistols) with specially designed blank ammo. It makes a specific sound and is designed to be as safe as you can get.
There are also rifle and even shotgun matches in the sport. Again, they both use pistol caliber blanks designed for mounted shooting. Rifle is considered to be an "advanced" aspect of mounted shooting. Riders are strongly urged to gain a level of proficiency with handguns before attempting rifle. On the "rundown" you will typically shoot rifle with two hands. That means the reins usually are dropped. Lots of fun, but harder than it looks.
Blanks provide NO recoil. If you try to shoot a .50 cal rifle off horseback - especially if you are not experienced in shooting from horseback - someone will likely get hurt. I am sure it is possible to shoot a 50 cal from the saddle, but I wouldn't call it advisable. I would strongly suggest against shooting ANY kind of live ammo from horseback. A small shift in the horse could cause you to shoot high. A bullet can travel well over a mile and kill someone. A mounted shooting blank is designed to pop a ballon at no more than 20 ft.
As I mentioned above, the best place for more information to do this SAFELY is to find a local club thought the SASS or CMSA websites. Mounted shooters are a very friendly bunch of people and will go out of their way to help new folks get into the game.
If anyone is having trouble finding a local club, feel free to PM me or post here. I know many shooters and trainers and will be glad to help you find one near you.
Mounted shooting can be the most fun you ever had in the saddle. It, like any other horse activity, can alsobe vey dangerous. At the very least, you can "ruin" a horse to this game by starting out wrong. At worst, you can shoot yourself, your horse or someone else.
The first rule of mounted shooting is "safety." The second and third rules are also "safety." Many others have made mistakes so we don't have to. Find a club and let them help you get up and running.