The biggest danger when the temperature drops well below freezing is freezing pipes. When water freezes it expands and can burst your pipes.
The first thing I do to protect my water pipes from freezing is to open the cabinet doors. Then I go to the refrigerator and take out the thermometer that I keep there to make sure that the refrigerator is working at the right temperature.
I put the refrigerator thermometer under the sink near the water pipes as they go down under the floorboards. This lets me know if the temperature is getting dangerously low to the point where I need to go to step two.
If the temperature is getting below 40 I start running the water every hour. I run it until the hot water feels good and hot. Then I run the cold water as well to make sure that it is still flowing normally.
Every hour I check the temperature. If it is getting close to 32 I begin running the water in the pipes. It doesn't need to be full blast. Just keep it running a little. That should keep them from freezing.
You might think that running a space heater near these pipes would help but the problem is not in the cabinet but rather in the space under the floors where the temperatures get colder still. Only heating your basement or cellar would help here.
If your pipes do begin to freeze you will notice that the water doesn't flow well. Just keep running the water and the water that runs through will begin to melt the ice.
If no water comes through you will know that somewhere the water in the pipe has frozen.
Locate the place where the pipe has frozen and use a hair dryer or heating pad to warm the pipe until the water begins to flow again.
DO NOT USE open flames or blow torches to thaw out frozen pipes. Doing this is one of the main causes of house fires.