Many barns, usually on a small scale, are always looking for help in exchange for some saddle time. However as Speedracer so eloquently put, it's not going to start right away. In order for you to ride, you're going to have to be taught.. and time is money so the owners of the barn will be expecting you to work your buns off.
Honestly I think you should maybe volunteer at a therapeutic riding center, horse side (or with kids too) so you can learn about the basic care and handling of a horse, then I'd look into taking some lessons.
The money you spend on gas alone to work for riding, and the amount of time you spend working will equal that of lessons, possibly more. In lessons you can also learn about particular things in depth, rather than have someone halfheartedly show you.
Most of the people looking for cheap labor do not spend a great deal of time teaching someone the basics of horse care. But you do get lucky.. and if you pursue this further I hope you find one of the good ones.
Hope that helped.