First off, I know how crazy horses can be! We have had one horse, and we had to get rid of her about a week after we got her (from a family member). She would not let the cows, or bulls eat. She would bite them, kick them, anything. They were terrified of her. You couldn't ride her.
As for firearms. We use an old Marlin 30-30 Lever Action. It works great. You can get shots off quick, it has great accuracy and range. I use my 12 ga. Wingmaster Super Mag usually. Some 4-6 shot works great to take down the coyotes, and, gives you a better chance at hitting them if they are on the run. My uncle swears by his 7 mm Mag. It is a little over kill, but has a great scope, and can shoot from a mile away if needed. Some people around here carry pistols also. .45, .22 are the ones that are used most. They work very well at close range, but when you are across a pasture they wont work very well. If you are a Fur Trapper and want to use the animals pelts to sell, the best way to go is a good .22 Long Rifle with a good scope. Great range, accuracy, and its a lot quieter than other guns so it doesn't spook the animals as much.