I generally leave the batteries in my motorhome and use the converter. Charging fully and disconnecting them in place would also be perfectly acceptable, but I appreciate having 12V power available in the motorhome when I want to check things out or exercise the generator or whatever. Some converters, mainly some single-stage converters, will boil a battery dry over time.
(Lead acid batteries are probably happier being stored fully charged at cold temperatures than at warm temperatures; the internal self-discharge is lower at low temperatures. If you have extreme temperatures, as in arctic temperatures, freezing could be a concern—but certainly not with New England temperatures, even during February cold snaps.)
Drain gate valves definitely closed.
Low point drains I generally close, though leaving them open shouldn't generally lead to much mischief. Same with the water heater drain plug—I put it in, but leaving it open wouldn't generally lead to trouble. There aren't many bugs out and about in winter time that would seek refuge in the plumbing.
For faucet taps, it really doesn't make any real difference whether they are opened or closed.
Leave one or two skylight vents cracked open (preferably ones with covers) to provide a bit of ventilation and help prevent undue condensation.
