Is your Camera a separate object to the Character and Horse? Or does each have their own Camera Component? Just to clarify, a high level description of what you want is; you have a Character (3rd person?) and you want them to mount a horse, which you then take control over, while keeping the same Camera your character uses. You do not want the camera’s to switch from Character to horse?
Why don’t you just use one camera then? Mount your character, lock it’s position to the horse, take control over the horse, no camera change required. I’ve not dealt with this myself, but this is how I’d approach it. Hope it helps.