We ran into a similar situation in our TT 2 years ago just after we moved to Missouri and were staying in our trailer while our house was being finished...in the dead of a bad winter for the area!
We stored water in containers for cooking, washing up and toilet use. Showers were a no-go. I could not find a way to keep an 18" section of the water system from freezing without major surgery to the rig. On the two mornings it happened, I braved the cold and took a shower in the bathhouse at the campground.
I think the 12 Volt heat pads, with insulation, are the way to go. Besides the typical RV types, there are a lot of different sizes made for commercial and industrial purposes. a search on Amazon can be useful.
Good Luck!
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