FWIW older gas water heaters that use a standing pilot flame and piezoelectric ignition can run without electricity. Combustion products are vented passively by convection. With this type, as long as you've got gas, you can have hot water. Maybe huddle by the hot water tank?

For the sake of efficiency, most newer gas water heaters need electricity for ignition as well as to power the fan that exhaust gases.

All gas furnaces will need electricity to run the fans.