Weight is not your friend off-road. I've been on diesel pusher winch-outs where a VW beetle would have driven right trough.
To be honest though, I though you'll have a much bigger problem with turning clearance and overhead obstructions. Most of the forest service roads here are pretty well maintained. Ground clearance can be useful for some of the drainages cut across them. They can get tight though.
To be honest, if you want to save on camping, you may be better off at Wally Worlds. A big motorhome winch-out can cost hundreds to thousands of dollars, depending how far out you are and how stuck you are.