There are several simple remedies to keep water pipes from freezing when the weather turns severely cold, as well as several remedies that can be costly. In either case, the idea is to prevent cold air from entering or to warm the area where cold air can't be stopped from entering. If pipes freeze check for pinhole leaks or cracks (after they've thawed) that can cause serious water damage to the home.
(Source: http://www.hgtv.com/home-improvement/tips-to-keep-pipes-from-freezing/index.html)
On extremely cold days, residents should take extra precautions to prevent pipes from freezing. One way to prevent pipes from freezing is to keep the water moving through the pipes.
To keep water flowing through pipes to avoid freezing, leave several taps turned on, with a flow that's just slightly more than a heavy drip. It's important to leave several different taps running, as sections of piping can freeze, cutting off the water supply to entire sections of the home (i.e. the entire second floor). Leaving several taps running slightly will also pull in more water though the main pipe running into the home - the pipe that is most likely to freeze in many homes.
A frozen pipe could burst due to thawed water to come pouring from the break. The following steps describe what you should do as soon as you discover a frozen pipe:
Thaw the ice in the pipe with a hot water bottle or hairdryer (taking care to keep it well away from any water), beginning from the tap end and working back toward the cold water tank. This will keep steam from being trapped by ice and bursting the pipe. With the faucet open, you can see when the ice has melted. Never use a heat gun or blow torch.