Your unit has a converter (as do most all RV's, if not an inverter/charger). The converter is basically a 12VDC power supply with battery charge protocol built in. Meaning it will ramp up the voltage to charge a low/weak battery then level out to a "float" level to maintain your battery. The enemy of a battery is extreme temperatures (hot and/or cold) and low state of charge. The converter will keep your battery fully charged giving it a fighting chance to survive the latter. So with all that being said. Leave your RV plugged in (to a 15 Amp "standard" outlet at home is fine) or pull your battery and bring it inside with a trickle charger hooked to it. Boy, that's a lot of typing . . .
BTW: I work at a Gulf Stream dealership as a Service Tech., your converter is suitable to properly maintain your battery safely. You most likely have a sealed lead acid group 24 deep cycle battery, right?