I'm not allowed to have a horse either. What we did do though is foster abused and neglected horses until they were healthy and trained enouh to be adopted. This has worked out really well for us and gives me my horse fix. Maybe you should look around and see if there is a rescue near you. Then talk with you parents about it. Your dad may be more willing if he knows it is for a good reason.
I agree. The horses at the rescue REALLY benefit from handling by a LOT of different people. There is no substitute for that, so you'd be doing a service, while getting your "fix."