There was a post on a thread recently about that. The fellow seemed to think it helped quite a bit.
I'm in the camp - leaving it on all day takes more energy than just heating the water when you need it.
The only thing I'd wonder about is where is the WH located - can you make sure the input and output water lines stay warm?
The water heater does have a direct opening to the outside temps, and metal conductive from the anode to bring the cold into the tank. Maybe a small electric heat pad to help keep the tank near the outside warmer.
Some others will add more ideas soon.
Not really my thing - you ain't never gonna find me camping at -31, no - change that - you ain't never gonna find me at -31 period.