Welcome to the RV world. You do not mention where you are in North America. I live on the west coast near Vancouver, BC so cold weather is usually not a concern. A cold winter might see the temperature drop to 5 degrees below freezing, but not very often. These kind of temperatures are of no concern for electronics, only to the plumbing! However, if you live in an area were it gets well below zero, then removing the TV might be a consideration. It would depend on how much trouble it is to remove the TV.
Happy trails, Knightly
2007 Itasca 35 ft. Class A, W24 chassis.