I don't have a whole house back up generator but I do have a quick disconnect on my furnace so I can power it off my 2KW Yamaha.
Last December 29th we had a prolonged outage with temps below -40 and over 100 homes and businesses froze up and had damage.
I was lucky and didn't have any freezing issues even though I didn't have the generator back then.
I keep my generator inside so I know it will start. Pretty sure it wouldn't if it was that cold out.