I commute to 35 degrees here and did to 5 degrees in Denver. No cold weather fade as I always have an over-capacity battery. It takes a while to cool down. In Denver I wrapped my office clothes around the battery to slow the cooling. If the light company has no suggestions post again and we can share ideas.

Batteries produce power by a chemical reaction. Reaction rate depends largely on battery design and chemistry. There may be a different battery type that works better for you. Try one of the big custom battery builders like House of Batteries in Fountain Valley, CA. (Disneyland area)