I don't know about a lot of legitimate backpacking but a lot of people go camping on the weekends. You may not get a lot of opportunities to do this as a 4/c because of limited liberty but you can definitely go somewhere over the long breaks. I went back country hiking in the Grand Canyon over part of a Spring Break my 4/c year and had a lot of fun. I've known a few people who did some hikes on the Appalachian Trail which is a little closer and had a good time too.