Cold weather is bad but when the wind is blowing as well is more likely that your pipes can freeze. The cold air infiltrating the tiny cracks around your house can cause your pipes to freeze quicker than it was the cold alone period. Think wind chill factor.
On the super cold days and nights do not turn your temperature down on your thermostat, keep it where it is. Keep the thermostat turned up to help protect your pipes and home.
Do not use your woodstove or pellet stove if you have one. Operating your wood stove or pellet stove will definitely warm up the area around the stove, but other areas of the house will become colder since the furnace will not be operating and blowing warmth to all areas of the home. I have a woodstove and my wife really loves it. However, on cold nights I do not operate it to help ensure that the areas of the home farthest away from the woodstove can stay warm from the furnace.
You may also want to actually turn up the temperature in your house by one to two degrees just to help keep pipes from getting too cold. Or do not allow your thermostat to turn down the heat in the evening on those really cold nights.
It is also recommended to allow the water both hot and cold water to slowly trickle out of your faucets. This help keep the water flowing. If you have a certain faucet that is positioned against an exterior wall or is farthest away from your heat source, then that may be the one to definitely keep running. I would worry less about a sink faucet that is strictly all the way in the middle of the house where it will be kept warm.
The expense of adding a few more degrees to the house on super cold days and nights is worth that extra cost compared to the cost of having frozen pipes and possible damage.
If your pipes do end up getting frozen, here is an article to help with that. STEPS TO TAKE WHEN A PIPE BURSTS IN YOUR HOME – Habitation Investigation (homeinspectionsinohio.com)