Is it okay to fire a kiln in the winter when the firing room is below zero F?
Yes. Turn the kiln on low for the first few hours so the kiln heats up gradually.
It is okay to store digital controllers in sub-zero weather. But before operating, raise the room temperature to 32°F (0°C). That is the lowest recommended operating temperature. Place a small electric space heater near the kiln's switch box to gradually raise the temperature there.
Some of the earlier controllers do not recognize a temperature lower than 1°C. You might look through your instruction manual to see if that is the case with your controller.