That's what my niece does (with my borrowed cable haha).That is really some clever ways to help them in the winter.
I did not run electricity to the coop. I think now that was a mistake. I have an extension cord running from the pool pump. I am bumping up against its limitations right now but I will get through the winter ok.
Next year I am bringing her 7 hens to my place, some of hers have frost bite on their combs I noticed today...