Your central HVAC system, heating, can run on a very small generator though, since the heat is provided by burning propane/NG/fuel oil.
AC needs electricity for the cooling itself too - lots and lots.
AC needs electricity for the cooling itself too - lots and lots.
My car can power a windowshaker and a refrigerator for days between charges. It can air condition itself for about a week. If things are at a place where that's not enough why would I stay there?