Having experienced numerous water problems at my current home, I decided to do what I could to thaw out the spigot and protect it further, since we were not to get into above-freezing temps for at least another day or two. I turned on a space heater inside the house on the wall behind the frozen spigot. Checked in an hour. Still no water.
Wrapped the pipe with styrofoam tubing, which I remembered I had in the garage. Waited another hour. Still no water, but I just had this feeling, I was getting close.
I had an "ah-ah" moment. Why not stuff the covers with alpaca and llama fleece? I had originally intended to card and spin these fibers into yarn at some point, but I thought it was worth the sacrifice to see if it could fix the problem. After waiting yet another hour, I went to check and water was already dripping! No busted pipe. No water leak.
I always knew alpaca and llama were one of the warmest fibers on earth, but I never dreamed I would put it to use in this way!