Follow the standard procedures posted everywhere for winterizing. I'd pull the batteries to take home and leave on a charger.
For theft-resisting (they'll get it if they really want it, especially if it's out in the woods by itself), run Kryptonite cables between slots in the wheels if you can. If you cable the front of the rear wheel to the rear of the front wheel, the former tries to rotate down while the latter is trying to rotate up so they tighten the cable and the wheels are locked. Get a good coupler lock that fills the ball area. If you can dig post holes under where the trailer frame will be and sink hardened metal loops into concrete in them (with 2-3' of dirt above the concrete), you can cable the trailer frame to the loops.
For critter-proofing, buy some aluminum window screen material, cut it into properly sized pieces, and stuff it deeply into ALL the openings underneath the trailer. Soak the ground all around where the trailer will be parked with insecticide like Diazinon. The problem with using rat poison is that you may take out some wildlife as well... your call. The biggest help will be to ensure there's no food left behind, and that all crumbs, etc have been removed.
Hope this helps,