Yep. Cowboy Mounted Shooting.
Tons of fun for the whole family. About 2000, the GA CMSA would come to the covered arena near me about 3 times a year to hold exhibition, and to let people try it out. They'd let you stand in the 1st group of balloons, and get used to shooting on foot, using their guns. And they would help you get your horse used to gun fire.,etc. Lots of foloks used gaited horses, like SSHs, foundation type Walkers, Foxtrotters etc. These were so easy to get used to the gunfire, and more level headed. Even Level 5 shooters used them a lot. WHen you got top the big events, like the national championships , there were long classes, using 45lc lever actions. This took a whole different kind of horse, and a very accomplished horseman, as you have to run the course using your legs and body. Your hands would be occupied with the rifle. Made alot of money training these horses for folks. Obama's ammo shortage about 2010 or so, put a damper on CMS for a while. Too expensive even if you could find it. I haven't paid it much attention since then, but I hope it is making a comeback. It is a very safe, very easy to get learn, and not very expensive, as far as horses go, to get into until you get to top level and want to do long guns. With the pistols, you don't have to have all that expensive a horse to do it. Back then, a pair of single-action 45's only cost about $800 or so. I haven't looked at them lately. If you like to shoot, and are an intermediate rider at least, with a horse with a good handle, I just don't know how you could have more fun than this.
Edited to add: Well, now that I think of it, the costumes required for competition cost a lot too. No Wranglers, you have to wear the authentic wool britches that button and have no pockets, held up buy suspenders. The button up shirts with no pockets and collars, with the leather cuffs at the wrist, No lace up ropers...has to be authentic boots., Same with the cowboy hats. Tack, holsters etc. have to be leather, No synthetic saddles, nylon bridels or holsters , etc.