No heat in my trailer, but I leave it plugged in.
As mentioned previously, a modern converter (or charger) is key to keeping the battery happy - leaving it in the cold or bringing in it is equal risk.
If you don't know what kind of converter or charging system your trailer has, you could pick up a "battery tender" or "battery buddy" from your favorite automotive / marine supply store and connect it to your battery directly. disconnect any other wires going to the battery first.
2013 KZ Sportsmen Classic 200, 20 ft TT
2020 RAM 1500, 5.7 4x4, 8 speed