What would one do in a situation like Sandy?
1. Do water changes on all tanks the day before problems are expected to start. Marine folks need to make plenty of spare RO and salt.
2. Have battery powered air pumps* and plenty of batteries ready.
3. Use a generator if you are allowed one where you live and your home allows you to set one up safely.
4. Bundle up your house to minimize heat leakage. Shove towels in drafty places. You want to preserve your warm air.
5. If you don't have a generator that can run heaters, bundle up the tanks with thick blankets/towels.
6. Use windows for light when possible if there are photosynthetic organisms at stake and the room isn't too cold.
7. Some rooms allow taking advantage of the greenhouse effect when it is sunny after a storm. If you have one room that's staying warm, obviously it's better to move tropical animals to that room even if it means putting them in buckets with only an air bubbler.
8. Don't feed tanks during a power outage to minimize waste in the water. Particularly if the tank is running cool, the animals will be more sluggish and food will not be a priority for them. Most tanks can easily survive several days without feeding.
*I recommend not using airstones with battery-powered pumps during an outage, since the pumps are not very powerful. Wrapping plant weights around open tubing to weight the ends down has worked best for me to get the most surface agitation and flow, and it's sometimes even possible to have one air pump service multiple tanks when used this way.
Small tanks are the most likely to suffer problems quickly. Large tanks, such as a 40 or 50gal tank are much easier to deal with than a 5 gallon. Similarly, a 500 gallon system will be even more stable for a longer time - public aquariums have this on their side. Also, a lot of fish an invertebrates can survive oddly low temperatures for short periods of time provided that the changes for both cooling and warming again later don't happen too quickly. I've had to go through quite a number of multi-day power outages in winter with snow on the ground and without a generator. I didn't have losses during those, so a power outage in the cold doesn't always mean death for aquatic life.
Something lengthy like a week-long outage is going to be a problem regardless of exactly how cold it is outside. During the last bad storm in my area that caused 7+ day outages for folks, some stores that had power allowed people to bring their more fragile livestock in for holding while they waited to get their power back. These were all pretty small stores that were family-run places who knew their customers well, not big chains.