Well, I live in an area where the power is often out. I don't have much for back up so if it's likely to go out, I heat the house a little warmer than usual so it will last longer.
Others have wood stoves or fireplaces. BUT if the chimney is iffy, be careful and make sure you have a battery powered carbon monoxide detector right with you. That is one way folks have problems with indoor fires, even with propane or kerosene heaters or gas stoves.
If you have a gas or propane stove, stay in that room and run the oven a bit. An old woman in Iowa kept her kitchen and a bathroom warm enough for days by heating unglazed clay plant pots (no plants in them!) on her gas stove. She would heat them up to red hot on the burners, then turn the burners off. The pots slowly cooled and kept the rooms warm enough.
Candles can heat up a small clay pot and if you put 3 or 4 candles together, you can heat up a pot of water, soup, or even fry an egg in a small pan over them (tip from my Gramma who lives in an apartment with all electric heat and appliances).
If my power goes out I have also been known to take a hot bath with the last of the hot water and leave it in the tub to cool. This does make the walls sweat, but I get that heat into the trailer. BUT< if we're going to be super cold for a while, that means I'll have to keep a hot water tap dripping or the water heater will freeze solid which would be very bad.
Hope you have heat and water through the storms!