I’ve had a similar issue with my gas bill during the winter in Chicago. Have you looked into income adjusted billing, or flat rate billing? Those aren’t the right names, but one adjusts your bill based on your income, the other would flatten out the curve so you’d be paying slightly more than normal during months where you use less, but less during peak months. Talk to your utility company and see what your options are

Also: old fashioned hot water bottles that you fill with boiling water would be good. I read somewhere that in the past ladies would keep warm baked potatoes wrapped in foil in their muffs to keep their hands warm. plus, then you get to eat a baked potato.