It does get cold here, but not cold, cold. Single digits maybe, but I don't recall it going below zero. According to an RV service person, they were told by a battery
rep that a fully charged battery
would not freeze (bet he wasn't from where you live, Joe!). If I still lived where it got cold, cold I'd probably remove it, but not here, though.
I never took the battery out of my vehicles when I lived in Wyoming, but I did plug my vehicles in at night. My battery never froze, but my truck gears did once.