The problem is that batteries can't sit outside when it gets really cold.If you have a couple hours of sun during the winter one could use a small solar set up.
Something like this - specwise.
https://www.renogy.com/200-watt-12-volt-solar-starter-kit/
Add a cheap deep cycle marine battery for $75-100. A small inverter for $25-75. Put a timer outlet on the inverter.
It would provide enough power to periodically run whatever water heater method you want to use depending on your sun hours in the winter.
And there is so little solar gain from solar panels in the winter.
I know batteries are getting better.....