Batteries are damaged by cold when they have little charge. When I leave one outside over a winter, I usually put a charger on it for a couple of hours once in December and again in January or February.
The real problem is continuous small loads draining the battery and making it vulnerable - a light left on for a week followed by a night at 30 below destroys the battery. Even little loads like a propane detector can drain the charge over time. The smart thing to do is disconnect the battery so there is no load. Don't rely on the battery disconnect switch; unhook a cable.
I did not understand that even deep cycle batteries should not be discharged much more than half way in regular use - that shortened the life of my first set of house batteries, which soon left us with no furnace in the early spring mornings. Overcharging can also reduce battery capacity. If plugging in to shore power for days at a time, I would make sure the converter charging voltage drops to no more than 13 after batteries are fully charged. If not, the batteries must be disconnected from charging, by unhooking if the disconnect switch doesn't do it.