For what it's worth, I used to pull our 4 T-125's, then got tired of trying to figure out how they all wired up in the Spring, so last winter I left them in the trailer, and the trailer plugged in. Didn't have any problem, and it gets pretty cold around here. As long as the batteries have a full charge on them, you should not have a problem either way, even in extreme temp. Otherwise, all our car batteries would be splitting left right and center.
Jayco Jayfeather 26L (2008) behind 2006 Ford F-250 SuperDuty. 480 AH Batteries, 300 watts solar, too many mods to list!