Volunteer work is different than paid work. However, the problem in many work environments are the insurance and liability issues. So, you would need to find some kind of place that is set up for volunteers already -- those are usually more accomodating for younger volunteers because they need anyone they can get. Perhaps a therapeutic riding stable? Perhaps a rescue organization? And don't limit yourself to horses. If you can get something with animals anywhere, that at least gives you some experience that you can bring forward to a possible position with horses in the future.