No lease to own. If you're willing, do payments but the horse stays on your property until paid off, YOU take out an insurance policy naming you as the payee if something happens to the horse and they pay for the policy, and they can come to your property to ride for the trial period. EVERYTHING is nonrefundable in a case like this. I don't do trial periods, leases, payments or anything like that. Buy the horse or don't, but once you sign on the line, it's yours and your problem.
Since you say you're ok with a trial period, then give them 2 weeks but require a 1/3 down, nonrefundable deposit and it doesn't start until the horse is insured.