I have enough flashlights, headlamps, and radios (amateur and otherwise), to supply my whole neighborhood. I keep enough gas for my generator for a day or three of intermittent use without siphoning the cars.

My primary emergency heat plan is to use the generator to run a (powerful) space heater and close up a room enough to keep us all warm. Unless it was super cold we could probably do without that for at least a few days.

I'm a good enough electrician to disconnect the furnace from the service and run it off the generator, but we'd have to be out of power for a long time, while it was very cold, without a viable bugout option, and with the gas service still working, for that to make sense. It strikes me as unlikely.

For those with generators: A reminder to never, ever backfeed your generator into your primary house wiring. Either use extension cords appropriately or have a licensed electrician install a bypass switch.