As of last year, there were only 2 cases of CWD ever reported in region R. Both cases were down in area 41. I don't think you need to worry about it.
http://gf.state.wy.us/downloads/pdf/...ary6-15-07.pdf
I don't think people will mess with your stuff if you leave it on your ATV, especially if you are on an ORV trail. Just to be safe, though, I think I'd put it all in an ATV bag to keep it out of the rain, and that way you could put a little padlock on the zipper if you're really worried about your stuff being stolen. Also, if you don't have a gun scabbard for your ATV, keep your gun in a case while you're driving. Otherwise you'll get dust all over it.
The game cart is a great idea. Especially if you're going to be packing the animal out by yourself.
Best of luck to you.