We made the run up the hill this morning to check for any damage. The part of the pipe in the crawl space that pops out of the ground and into the house under the kitchen sink was frozen, even with the electric heat tape on the pipe. So I have no running water. At least there's no major pipe rupture, although there could be a leak after everything thaws. I originally thought that the heat tape was defective, but I tested it tonight with a bag of ice and it works fine. I believe the problem was that I located the heat tape thermostat on the part of the pipe closer to the house instead of closer to the ground - so the thermostat was seeing the warmer temperatures from the house heat warming the pipes, and the heat tape wasn't turning on when needed.
