Last winter in Minnesota, my heat pump gave out at -10 degrees. I felt so smart for going green (and maybe a bit too proud) until I was huddled by a space heater. That backup system is no joke, and my electric bill that month was brutal. Now I keep a stack of blankets and a prayer for the grid handy. It's a good reminder that tech fixes need real world plans to work.
My cousin in Duluth had the same thing happen. His heat pump just quit at minus fifteen. He ended up using a kerosene heater in the garage for a week. That backup heat really does crank up the meter.
My buddy in Maine had his heat pump freeze up last January, just like @the_blair said. He was stuck running electric baseboard heat for days and his bill looked like a phone number. Makes you wonder about putting all our eggs in one basket.