Yes heat your house, for many winter storms knock out power for a day or more and if it is 32 or lower out your house will be in the 50s after a day or less. No inverter will help then without heat.
I live up in Canada, we know about winter storms I tell ya!
Thought about going generator, just don’t know enough about them. I can live with the house hitting 12C like it did during the Niagara ice storm last year, pipes stayed in the safe zone, but more worried about the reef. Maybe I’ll ask my HVAC guy if there’s a generator solution that taps into one of our unused Nat Gas valves.