I picked up two used enclosed cargo trailers like Jose stated above and saved a bunch of money. Both are flat front (not V-Nose), one is a 6x12 single axle with barn doors and the other a 7x16 tandem axle with drop ramp. Ground clearance isn't really a strong suit of enclosed cargo trailers, they are pretty much made for pavement use. I drove into the mountains with the single axle when there was no snow on the ground, then drove out a week later with snow on the road. The trailer wheels were wider than my Suburban wheel tracks and the trailer had a tendency to try moving the vehicle around on the switch back roads (under the influence of deep snow and mud).
I don't have an ATV, but would recommend camping with the trailer at an established camp area and driving in deeper (up) with your ATV. The height of your side by side will be the key to trailer size, it'll take a pretty tall trailer to allow room for the roll bar to clear (my father-in-laws Honda MUV700 Big Red was too tall to fit into my trailer). I'd recommend a tandem trailer with adjustable (height) hitch so you can get it level with the receiver on your vehicle (versus drop hitch on your receiver). My tandem trailer is a "Work Force" brand (made by Wells Cargo) and is very nice. I can't imagine pulling something much bigger than a 7x16 into the mountains (at least not very far).
Mine doubles as a way to move our kids to/from college each year. You can pick their stuff up from college in May and leave it in the trailer until August, then it's empty come hunting season. I've seen a couple trailers on this site where guys converted enclosed cargo trailers into some cool toy haulers/campers. Check them out, some good ideas for sure!