Check with the Forest Service on camping. I hear they are pretty strict down there about off road use and having to stay in designated campsites. Also be advised that is the area of the state where CWD (chronic wasting disease) was found so you might have to do mandatory testing. Check out NMDGF
for online rules and regs from the G&F department. Click on the rules booklet and check out page 42 on deer and page 79 for elk. I don't think testing is mandatory anymore but I could be wrong and they give you an incentive to test. You could be coming back for an Oryx or elk hunt.