Many people believe that their furnaces malfunction when the temperature outside drops, but the problem may be infiltration -- outside air seeping into the home through attics, windows and doors and continually lowering the home's temperature. The situation makes the furnace work longer and harder to increase the temperature. That is not a furnace problem, just a natural reaction due to sealing issues with the house.
If a heat pump supplies warm air to your home, then you may have noticed that part of the heat pump is outside.. Snow piling over the heat pump's evaporator coils can cause the unit to stop working properly. The coils also may produce condensation that can freeze in ice layers until the furnace is unable to transfer heat efficiently.
Heat pumps use warmth in outside air to heat inside air. If the outside air is very cold, however, most heat pumps use a secondary system that have an electrical heating element. If the heating element is broken or its wiring fails, then you may find that out only when your furnace stops working.
Geothermal pumps attempt to solve the problem of cold outdoor air by drawing heat from the ground. They use underground water to absorb the heat. Unfortunately, underground water also is affected by cold temperatures. That may not stop your geothermal furnace from working entirely, but, like infiltration, it slows affects how well the furnace can heat your home.