Cutting the grass down is a good idea. The tarp can help with moisture coming up from the ground but it will kill the grass so check with the property owner first. Mouse traps can hurt other animals so watch what you use and any bait for traps WILL attract other animals like raccoons so don't use any bait. The jacks are only for stabilizing not to lift the trailer of the suspension. You need to remove anything you worry about freezing and any food.
I would also park it on some treated wood boards like 2x12 long enough for both tires and raise or lower the front so water can run off easier.