Generator. Unless you have a healthy sized battery bank, a 12 volt inverter won't cut the mustard. Then you need to recharge the batteries if it lasts more than a day or intermittently. I always have a couple of gallons of fresh gas that gets rotated, so the genny can always be fired up. Preferred source of heat would be a wood burner but I don't have that setup. I can disconnect my furnace from the power panel so there's no backfeeding into the grid and injuring anyone. A freezer will keep cold for at least 24 hours if you keep the door shut. If it's cold enough outside, frozen food can be stored in containers outside, same with some of the sutff from the fridge.
Remember that whatever a 120vac appliance uses in amps, it uses 10 times that much on a 12vdc inverter. That doesn't include the extra start up draw on motorized items, such as compressors for fridges, freezers, furnaces, water pumps, sump pumps, etc.