It's not that simple of a question. I used to go jogging at -20. I'd wear a synthetic hoodie (cinched up sometimes) and a wind shirt (and mittents, pants, etc), but no face covering. Ice would form in my beard, exposed hair, and eyelashes (which is probably what people mean by their eyes freezing - eyelashes can freeze shut), but my face was fine.

Wind can certainly make a huge difference. I've spend a lot of time outdoors in the Arctic and subarctic - only time I've dealt with tissue damage was on day that was about -10 but had 30 mph winds. Fucking awful.

If there's no wind and you're staying active, it's not difficult to stay warm even at very low temperatures.