This may have been posted before but I see questions about it everywhere: How do you stop your horse following you into gunfire when it's not getting scared of it? (this is probably another glitch)
Equip your fist, and without pulling the left trigger point yourself at the horse and pull the right trigger, you'll give the horse a harmless push which will make it run off.
sidenote: this same push can be used on civillians to start a fight, or clear a poker table (all players run away, but run around the block and one or two will be back which makes getting the US army outfit faster than cheating/dueling.
Edit: I agree with the staff: this game is incredibly rotten about conveying shit like this! The mission "Justice in Pike's Basin" (the one shown in the quicklook) would've been an easy way to show this if the marshall said "Slap the asses of your horses lest they catch a bullet boys" prior to heading into the combat part of the mission.