I agree with the lessons as well. Most horsey people are spread thick enough that there are lesson barns in or near most cities. Also, I find that most board or lesson barns have show schedules posted pretty prominently, perhaps you could watch a couple of shows throughout the season. I find that most small shows are pretty despereate for gate crew/ring crew help, so if you get bored watching you might get involved there, too. The rescue voluteering is a good idea, too. I volunteered at my local vet's office as well, both with small animals in the clinic and with horses and cattle on farm calls. Mostly watching and cleaning up, but it was fun. As a junior leader in 4-H I might also suggest looking into a 4-H club in your area. I was lucky and able to borrow horses for 4-H shows and activities until I got my own, but 4-H does offer a "Horseless" program as well. The "learning" and workbook part of that I found a little cheesy at 14 years old, most of that is geared toward the youngest end of the 4-H member spectrum, but it gets you around and learning about horses and minimizes those withdrawal-like symptoms between lessons.
I also met some of my closest friends (human and equine) through 4-H.
There are lots of ways to get involved. Sometimes a good way to start is to just do a Google search "Horses (insert City/state here)".