If pipes go through unheated areas of your house and you need to leave a tap running so they don’t freeze, you should invest in some insulation for those pipes, as the cost of the insulation is usually less than what it will end up costing you to run the water throughout the winter, especially in colder climates.
The easiest way to do this is to use pipe wrap insulation. It looks like a long tube with a slit down the side, which enables you to wrap the insulation right around the pipe. They come in different diameters so check and see what size of pipe you have before you go out and buy the pipe wrap insulation. Then simply use duct tape to secure it at each end.
You can also use insulation tape for pipes, if it is just a small area that is exposed.