Ive got no problem going 1 night in freezing temps with the stupid little battery FR puts in this beast
2 nights is pushing it if temps are below freezing
If the vehicle wiring is proper, as is the trailer, it should charge 100% while the vehicle is running, but it will take some time. its not going to reach a full charge in 20min, or even an hour due to the voltage drop between the power source and the battery
if the battery is in good condition (it could be a year old and be f'd, or 5 years old and be at 98% capacity), one night on battery shouldnt be anything to even think about. but whenever possible, it is better for you and your batteries to go overboard and have more than what you need in order to reduce sulfation in the batteries and damaging them(due to excessive discharge), and waking up freezin your butt off because the furnace wont kick in LOL.
If i was you, i would plan on going to a larger single battery, or even going to a pair of identical 12v batteries, or a pair of 6v in series if you plan to do this often (increased amp hours, but they can be a PITA in the long run)