The colder it gets outside, the harder your furnace must work to keep your home at its usual average temperature. That's an unavoidable consequence of the fact that more heat flows between a hotter object and a colder object as the temperature difference between those objects increases. Your house is losing heat faster in the cold weather so your furnace must produce more thermal energy to replace what's lost to the great outdoors.
However, it's quite possible that having the furnace run more often makes your home feel warmer. If you spend much of your time near the radiators or heating ducts, you'll feel the furnace heat as it enters the room and the more time the furnace spends heating the room, the warmer you'll feel. Overall, the temperatures in your home are probably becoming quite uneven in cold weather. The air is warmest near the heating system and coldest at the outer walls and ceilings where the heat losses are most severe. You might be able to make your home feel warmer all the time by circulating the air better. Also, hot air rises so adding a ceiling fan could help by sending the warmer air that accumulates up there back down to the parts of the room where you actually live.
Answered by Lou A. Bloomfield of the University of Virginia.