The car is overheating and only cold air coming from the vents. Sounds like to me your thermostat is toast! Try replacing it first and work from there. Pearl02.
I agree, replace the thermostat and flush the system with some hot water. Then fill the engine, replace the thermostat and fill the rest of the system. Leave the cap off of the resevoir and start the car to burp the system.
The thing that puzzles me about the thermostat is . . . why would it only act up in extremely cold weather? With a thermostat that was stuck closed, I would expect the car to overheat on both hot and cold days. That's why I am going with the freeze-up theory.
Years ago (before modern coolants were invented), on sub-zero morings it was common to see numerous cars stopped along the road with steaming radiators.