While there are plenty of Alaskans choosing to live without power and running water most of us on the road system here have such luxuries.
I know there is the reality show in McCarthy where they raise animals off grid.
But I don't know about chickens.
Of course it matters not to me as I have power and choose to use it.
I work in the extreme arctic flying to work for 3 weeks then flying homework 3 weeks off.
Chickens would not survive there in wintertime. But not just because of lack of light.
It gets real cold and real windy.
Long periods of both.
I've only seen -62*f personally but know others have seen -80*f.
I've seen wind chills down to-100*f and colder.
Also ground blizzards are common there.
Any crack will see snow infiltrate.
Whole pickup truck cabs packed full because a smoker left a window cracked 1/4".
So your coop couldn't be ventilated traditionally.
Plus the storms last for several days sometimes.
Here's a good picture of my work truck after such a storm.