When clicking on a horse, it will sometimes cause your character to become “binded” to the horse. Your character pretty much becomes a ghost, only blocks close your horse can be broken, mobs will target your character on your horse, and kill you. You can only right click things and kill yourself with bushes or drowning as the ghost. Other players will see you on your horse although you may be somewhere else entirely as this “ghost”

The only way I’ve found to fix this is killing yourself (logging out doesn’t work) and after you die your horse becomes a fake entity. You can’t hit it or move it, it doesn’t move, and if it’s on a lead, the lead will permanently be attached to the horse unless the horse manages to die if it gets out of its “fake” state