When someone asks about bateries over winer there is one question I ask
WHAT CONVERTER DO YOU HAVE
Progressive Dynamics Charge Wizard controlled (9180 with wizard, or 9280, or one of the other models eitehr with optional wizard or built in wizard)
By all means plug in, leave batteries in RV and connnected,, Check fluid level before storing, Long about New Years Day, and again in spring.. NOTE: Do not add in winter less it's above freezing. and staying that way for at least 48 hours.. Or pug light bulb in battery bay (plugged in, Incandescent 100 watt) to keep batteries above freezing for at least 48 horus.
IOTA with IQ-4.. See above
WFCO: This unit has a high failure rate but USUALLY fails safe so I'd say keep it plugged in
Parallex 7300... Likely will be OK plugged in but you really should upgrade.
Magnetek 6300 (no longer made, bought out by Parallex and upgraded to the 7300 which is worlds better) UPGRADE.. This is not an optionm, UPGRADE
If Upgrading look at Progressivew Dynamics 4600 series.