How-to
How to Keep the Heating System Reliable Through a Cold Snap

The furnace that quits does it on the second morning of the cold, when every shop is already booked. Run it while the weather is still ordinary.
The day before
Set the thermostat to heat and let it run ten minutes. Listen for a rattle that was not there in November. Change the filter if you cannot see light through it. On a heat pump, brush snow off the top and the sides so the fan can pull air. Do not shovel the driveway onto the coil. A unit buried on one side will ice up and sit in defrost. That fault is the same one covered with older heat pumps.
While it is cold
Raise the setpoint two degrees at a time, not eight when you walk in. A big jump runs backup heat for a long stretch, and then it feels like the system gave up. If the furnace starts, stops, and starts again every few minutes, stop resetting it. The checks are the same as the morning it will not start.
What not to plug in
A space heater on the same circuit as the furnace will trip the breaker and look like a dead furnace. An unvented heater in a closed bedroom is a carbon monoxide problem, not a backup. Another blanket and a clear filter beat both.