Your breather tube froze up.
Pretty common, but not something you want. It’s happened to me in the past, but it’s curable.
Moisture that should have gotten out of the tube and recycled back into the intake was able to collect in the oil instead of steaming out.
There’s three solutions.
1) Bypass the breather tube. Simply disconnect it from the air filter box (and plug the hole on the air cleaner)
2) Run the generator in a tote or under a tonneau cover so it stays warmer
3) Buy the fancy Honda cold weather kit. It’s basically a tiny heat tape for it (and not cheap).
Another cold weather tip, remove your air filter. Blowing snow can plug it up when you least want it to. Just make sure to put it back in for the summer months.
Hope this helps!