A road that is plowed and salted enough to safely drive a car is clear enough for me to drive a bike too.

As for cold, the kids can stay under a bubble canopy if it's really bad. I have this bike, though we've never bothered with a canopy, we just dress them warm (in New England): https://www.google.com/search?tbm=isch&q=workcycles%20kr8%20...: