Right now you gotta aim yourself sideways in order to enter a house or a cave on a horse, cause your characters hitbox has to touch the door's hitbox. This not only looks weird, but also likely something that newer players will not know with no way of learning this unless someone tells them that, or by an accident. Moreover it has no logical explanation that is not "this is how this game-engine works".
So please just make horse hitbox act like your own hitbox in terms of entering and exiting things when you're mounted!