I've had power outages in winter of up to a week. As long as there's enough warmth (through propane heaters, space heaters run by a generator etc.), absence of much light for that length of time doesn't cause lasting problems. Several weeks, and you'd have leggy plants and other difficulties without moving plants to windows or using a supplemental power source.

I would say you should keep the plants as cold as possible to minimize any impact. Tropicals at 55 F, and other plants at 40 degrees.