I would removed any food, bedding, towels, throw rugs. If you have mice, they will use any loose fabric for bedding, they may also tear into other fabrics that you can't remove, so you do want to do something to try to prevent them. Have heard Freshcab mentioned a lot. Haven't researched to see what that is.
We did not remove our battery, used the battery disconnect switch and the house battery which was older was bulging/had frozen and we had to replace it. Engine battery was fine and the coach started right up. If we were to store it over winter again, we would remove both batteries and store them in a warmer place.