Dan,
We could do the math, but my guess is that keeping the fresh water tank "warm" is beyond the battery capacity you have available (I have four batteries, solar, and an enclosed under-belly and I am confident that I couldn't keep my tank warm enough, for the temperatures that I use our trailer in, with just battery power alone). However, because of it's thermal mass (assuming it's not almost empty), your tank probably wouldn't be the first freeze anyway. Rather, it is likely to be any exposed water lines that would freeze first. And this you "might" be able to protect by:
- circulating the water (I still suggest adding heat via your hot water heater while you are at it)
- insulation (right around the pipe)
- Heat heat tape, preferably right under the above mentioned insulation. 120 volt heat tape "should" work as it's just a resistor. You just have to de-rate the amount of heat you expect to get (and the energy used) by a factor of 10....might be worth a try anyway. Of course, using it this way would likely void any manufactures warrantee .... blah, blah, blah.
If you really want to protect the tank, and you don't want to try to insulate (and heat) the whole bottom of the trailer, perhaps you could fabricate an insulated box that encases just the fresh water tank. Then, you could even put a 120 volt heat pad (de-rated by 10) or use other ideas others have given you for low wattage solutions, right on the bottom of the tank to provide some "minimal" amount of BTU's to the tank. Doubt it will do much other than drain your battery, but at least your tank will be insulated....which will help a whole lot.
Have fun with your project.
