Thanks MrsD - I hadn't heard of heating tape.
Unfortunately my water pipe's buried underground where it runs from the water pump shed into the house - only a distance of about 4 yds but enough to freeze. Normally happens only a few days each winter - it's unusual to have 6 days in a row with sub-zero temps as we've had this past week (warmer but wetter today). The above ground section of pipe is insulated with lite density foam wrap.