No need to tell me; I’m not the one in the OP’s hypothetical situation.
But if I were, I would quickly find a release form and have it signed before anyone got on a horse. My experience is that many BOs/BMs rely on very non-hypothetical contracts and make riders sign a very non-hypothetical release form for their protection.
The OP would have to contact a lawyer to define whether the horse owner contracting privately with a horse rider to give lessons to a private party, on the horse owner’s horse, would put the barn at risk, if a release form had been signed.