Hoping you got this resolved. I live in Upstate NY, I had similar cold weather starting problems with our 4390-2 generator when the outside temperatures dropped below 25 degrees. Our unit is NG. Checked pressures of flow, adjusted valves, tuned up, checked choke plate, checked battery and actually replaced it with one with higher CCA, etc... Nothing, would work fine when techs checked it out usually in the warmer temperatures of late afternoon. Wouldn't run the next day in the morning after a cold night. Started failing to start during weekly test run. Replaced the sparkplugs with new plugs and tightened up the sparkplug gap. That was the final solution. Worked fine after that. Started to act up again after a couple of years. Changed the sparkplugs with the same tightened up gap, worked fine again. There are several threads on sparkplug gap. I'm not saying this is your problem, but might be worth a try. Hope this helps.
That's a sign that the ignition system is weak.
Could be coils, plug wires, or the coil drivers, or even the plugs themselves.
I'd try a different brand of plug first.