I’ve run an AC for two weeks on a generator, but if it’s a real SHTF just get used to the heat. AC is not a necessity.
I grew up without ac but houses were built for it back then. We got our first AC, a window unit when I about 11. Within 2 years we had central heat/AC.
The problem with my current house is it was built in the age of air conditioning. The windows are double paned and difficult to open. When you do open them, there is just a small area open. It also has a fairly low ceiling.
Our old frame house had shade trees, (live oaks) all around the house and I could open a couple of windows in the Summer and the breeze would often get just a little cool by morning.
I live in the Florida Panhandle and Winter is no problem. It gets cold but I can always sleep under blankets.