My barn allowed people to work around the barn if you are 12+ so I'd look into that.
Braiding for your barn and others at a show. I'm 14 and braided one weekend and earned 80 dollars doing one horse
babysitting works pretty good. Or if you prefer animals over kids, you could dog sit!
i have the same problem.:(
At that age it is very difficult to find jobs like being a groom or mucking stalls as typically people prefer 16+ for that.
I've been in your spot, and at that age I mainly did odds and ends type jobs. I would take care of dogs for people, mow lawns, that type of things.
If you have good standing relationships with trainers/barns you can ask to do work-to-ride type programs which basically allow you to do work (barn chores, stalls, clean outs etc) in order to gain lessons/board discounts/Horse time.
I hope this was helpful!