[Festus2]

If you leave the battery in your unit, plug into shore power and use the converter to keep the battery charged, you will need to regularly check the fluid level in the battery so that it doesn't get too low and leave the plates exposed. Leaving the battery without checking it over the whole winter will likely result in this happening. Come Spring, you may find yourself with a battery that is completely "dry".

If the battery is kept in a fully-charged condition and the fluid level maintained, it should withstand sub-zero temperatures.

If you are leaving the battery in just so that it can be charged by the converter, it makes more sense to remove it, take it inside and put it on a trickle charger over the winter.

Depending upon how you have your quick disconnect "connected", it may not be able to be charged by the RV's converter.

I'd be tempted to take the battery out and leave your unit unplugged.