Eskimo,
My wife worked for 3 months at a hospital in the northeast, and they had to implement some fairly extreme measures anytime the temperature dropped below zero due to some deaths. You can't lock exit doors, but that means occasionally you'll get a patient who takes a wrong turn and winds up outside in the cold at night in an alleyway behind the hospital annex. They had an elderly and slightly confused patient and a "merely" sick patient exit and die from exposure halfway back to the front door... There is no way to hold every patient's hand 24 hrs a day, no way to guard all exits, no way to confine patients to certain areas.
Schools are the same way. You can't watch every single kid every second, not with the level of school supervision nowadays since every volunteer must go through a federal background check and meet other strict requirements. So if there's a chance a kid is going to be found frozen solid out by the dumpster, they're going to be inclined to close the school whether it's in Alaska or South Texas.