You need to rely on your battery less. Resistance heating like a hair dryer, microwave or an electric blanket use a lot of current. Running the furnace all night requires around 5 amps when it is on. Best to think in terms of extra blanket, down comforter, down bags. With the trailer closed up it will not get that cold.
If you really want to use a TV, lights, electric blanket, etc. then you need two batteries or more that can take the drawdown of all of that use. That usually means AGM or lithium batteries.