I've left mine in the van, disconnected, for the last 3 years (was new then) with no problem so far, its just topped up regularly over the winter to keep the charge up.
I only disconnect for safety incase some rodent friends find my can and chew on the cables.
Our display engine has two 12V 105AH Sprinter batteries for the electric start, and that sits outside under a sheet all year round with no special treatment.
As long as the batteries are in good condition, fully charged and topped up if necessary, they'll be fine.
The trailer has two 80W solar panels to keep those batteries up on charge, or we can plug the EHU in and use the on-board 26A charger.
Did look this up a while ago and posted here. Even a fully discharged battery would need to drop to something like -40 before it would freeze. A fully charged battery was about -80 iirc so freezing is not an issue, if it was then they would never start a car in cold climates.
The bigger issue is letting the battery discharge too much. A fully discharged battery may never recover, even dropping to 50% will reduce it's capacity and life expectancy. Either take the battery home and charge it occasionally or fit a solar panel. The solar panel is the better option as it enables you to use sites with no EHU which are a lot cheaper and easy to find a vacancy without booking even at the height of the season.
A day of all things motorhome and campervan. The show is held both in the main indoor arena and across the grounds. Catering, hot drinks and food options are available. Easy access to the site and free parking included. Win one of five pairs of day tickets