I'm thinking that the types of temperatures you experienced wasn't the cause of your battery depletion and the furnace not running.
Do you have a battery disconnect switch? How are the batteries maintained while in storage? Do you have a handheld meter?
Sorry, lot's of questions but the answers may lead you to the cause of your batteries being depleted.
FWIW, I've experienced a lot of cold weather activities using batteries and if using completely charged batteries, there is little difference in their use until you get below 0f. At -10f, there starts to be a barely discernible difference and at -20f, batteries that are not charged fully become problematic.