I have both a wood stove and a wood burning fireplace. The backup was part of my justification for getting the stove. I don't know if it would be sufficient if I lost power for an extended period of time in really cold weather to keep pipes from freezing but you can't guard against every eventuality. (I also worry about what can happen when I'm not around.)
As for the food, I'm close enough to civilization that I'm not too worried. Worst case I get snowed in for a couple of days. I won't starve.
As for food: stock canned goods for a week. (There's a reason preppers have rooms full of the stuff.) You probably also want to stock bottled water for a week, just in case.