Hope this helps.
First how cold will it get? Also what do you plan on towing it with.?
Having it plugged in only provides power. If it gets at or below freezing you will need to use the propane or space heaters to keep the interior and underneath bays above freezing if you have water in any of the tanks.
Also depends what type of trailer you are looking at. If you live in a area that gets at or below freezing and have someone occupying the trailer you will need to have a 4 season trailer, which provides better insulation than others. Even then pipes may freeze depending. Most 4 season trailers have tank heaters so you should make sure what you select has them.
I've owned Arctic Fox (Northwood Mfg) 5th wheels which are considered very good trailers, and still had my disposal valves freeze. Better insulated trailers equals more cost and a heavier trailer.
Take your time and do lots of research before buying. ABOVE ALL "DO NOT BELIEVE ANYTHING A SALESMAN TELLS YOU"
Do your own research!