It's never too late to safeguard your plumbing against freezing temperatures.
Many people think that the ice itself causes pipes to burst, but the Building Research Council of the University of Illinois has shown otherwise. Water pipes in your home can burst after freezing temperatures create ice in the pipes. As ice continues to form, water trapped between the blockage and your faucet can be subjected to tremendous pressure. That pressure looks for the weakest point in your system in order to escape, which is usually a small weakness in the line, causing the pipes to spring leaks.
A temporary measure is to allow the faucet to drip slowly during freezing temperatures, which isn't a long-term solution and wastes water. While doing so may not prevent an ice blockage, the open valve can prevent the pressure from building up inside your pipes. If the faucet stops dripping, you shouldn't close it as it may still be relieving pressure from the system.
Pipes, especially poorly insulated pipes, that snake through attics, crawl spaces, or exterior walls are most likely to freeze. You probably have a frozen pipe if a faucet or appliance relying on that pipe isn't getting any water.
Regardless of where you live, you should wrap pipes with insulation. You can visit your local home improvement store and purchase very inexpensive foam pipe wrap. While you're at it, wrap any hot water pipes that are visible in order to reduce heat loss, including those leading to and coming from your water heater. If freezing pipes are common where you live, you may consider installing electric heat tape and turning off water to and draining outside spigots. In addition to wrapping your pipes, you should ensure that the attic or crawl space is also properly insulated. A few degrees can make or break your pipes and insulation is very inexpensive considering the amount of damage a small leak can do to your home.
Ironically, burst pipes are more of problem in the South where building practices are sometimes inadequate to protect pipes from occasional sub-freezing temperatures.