If there is a fixture in your house that is not getting any water during a deep cold like this, chances are you have a frozen pipe somewhere. Frozen pipes do not always lead to burst pipes, but that is always a possibility. For frozen pipes, the best thing to do is to turn the heat on to that area. For example, if there is a frozen pipe leading to your kitchen sink, open the cabinets beneath the fixture and allow more heat to flow to that area.
Pipes that are run on an exterior wall tend to be the first to freeze. If you have a kitchen sink or bathroom sink that faces an exterior wall, keep those pipes exposed to heat. You can also leave the faucets on at a slow drip throughout the cold. This can help curb pipe freezes.
If you have never had your pipes freeze, remember that (at least here in Ohio) we have not seen sustained cold like this in many years.