It probably goes without saying, but clean out anything that looks like food to a mouse--empty the kitchen cupboards, etc. An unheated trailer with no food is far less attractive to a critter than a nice warm one with oatmeal or whatever.
I set the plain old Victor mouse traps in my motorhome while its stored. Over the few years I've had it, I have caught a total of one mouse (and they're very much around in the semi-rural area I live in). It also appears I got him or her before there was any damage done...at least, I've seen absolutely no evidence of chewed or fouled bits.
While it's hard or impossible to seal every hole in a trailer, it is relatively simple to keep track of the possible entry points: they have to either climb a wheel, the tongue jack, or (if plugged in) the power cord. The more proof you can make those points against climbing aboard, the better off you're likely to be.