[Bill]

I used the black pipe insulation, and then used a larger diameter of pipe insulation wrap over that, then wrapped old rags around the spigot and horizontal line going into the house
I wrapped all that in an old comforter, then covered the whole thing with a thick contractor garbage bag to keep it dry and out of the wind.

Aero used the heat tape, under the pipe wrap, which also seems like a good idea. And now that you know where your weak points are, run those adjacent inside taps periodically through the night.

I suspect that's a lot easier than going outside with a hair dryer or heat gun to thaw the exterior piping.