Mike is on the right track concerning the entrance point on where the little buggers are getting in. They are looking for a warmer place to nest. If you want to investigate, use flour dusted on the floor around where you might think might be an entrance point. Look for little mouse footy prints in a couple days. Find that entrance point and seal it off.
Get all edibles out of the A-frame. Any food source is a magnet for them. Mice will be less likely to nest where there is no food source.
As far as getting the ones that are already inside, or know the way in (until you find and plug the hole), the jury is still out on that one. Search the forum. Many ideas and threads, depending on your humanity level, to get rid of the pesky rodents that already know where the "Bed and Breakfast" is. After that, it's just a maintenance issue to keep them out.
My TT is permanently parked in the woods. No 120 volt for electronics. Battery or genny for power only if I'm there. Otherwise, the TT is dead. Lots of field mice. I do the same routine every year for winterization. Only had an issue one year (out of 18 years). Figure out where they are getting in, seal it, maintain it for the Winter, and you should be fine from that point.