If you have a condensing
(means it drains water)gas furnace and your heat isn't working during these really cold mornings, more than likely your drain is froze up. If it freezes your furnace will shut down.....you need to take a hairdryer and thaw it out.
A permanent fix would be to run a french drain. If you have a Heat Pump and it's froze up there isn't much you can do but turn over to aux. heat strips. When a heat pump goes into defrost and it is so cold out, a lot of times it won't defrost but just keep freezing up more.
The heat strips will run up your power bill but you will have heat. I'd suggest a backup propane heat source like a monitor or free standing fireplace. If your power goes out, you won't need it unless you run a heater with a fan. Just a couple tips this cold morn.,I'm at work (hvac) and the phone has rang constantly.