I vote for removing the chassis battery and store it in your house or non-freezing garage. Clean the terminals, add distilled water if needed, charge it up completely, and rest easy through the winter.
That is unless you feel the need to run the chassis engine every-other week. If that is the case, idle the chassis engine for a half hour with only your heater on to dry out the interior. That would maintain the battery as well as minimizing any musty odors. If doing this, have all your cabinet doors open so the cabinet interiors also dry out.
But plugging in and relying on your on-board converter, typically won't do it. RV companies are real good about isolating the chassis battery from the house batteries so if you kill the house batteries, you can still drive away.
There are modifications that are often done to maintain all your batteries while being plugged in via controlled by an added switch or modified switch, but that is another topic.
