Are 당신 old enough to be able to get a job? If your parents' reason against 당신 horseriding is purely due to money issues, then maybe 당신 can find a way to make the money yourself. If 당신 are not yet old enough to be employed 의해 a company, 당신 might be able to do something such as walk 개 for your neighbours?
I think your parents would be really impressed if 당신 are able to earn the money to go riding, plus it will prove to them just how serious 당신 are about wanting to ride.
Good luck and I hope things turn out well for you. :)