if you play as a horse there should be an enemy type who looks like a traditional video game protagonist who tries to tame you and make you their mount, and if you lose, you have to do that character's errands until you can find an opportunity to knock them off or kick them in the head and escape
If you don't kill them then at any time they can summon you to wherever they are and then you have to fight the controls if you want to go anywhere else
When you encounter other tamed horses, if you kill their protagonist, then they can join your herd of evil horses. (At this point I have literally just convergently evolved the premise of Roger Zelazny's "Devil Car" oops)