Yeah, I'd agree with that. Road clearing in general is pretty bad here, let alone sidewalks and bike lanes (especially since the "clearing" often involves pushing it off to the side and blocking up those lanes).
I found it cool how some countries had sweepers which collect the snow and cart it off rather than just pushing it around
The one in the image here is an electric assist, hills are no problem. If you wanted to get it to work in the winter you could buy an electric assist trike. The bucket in the front is wide instead of long. A family in my neighbourhood drops their kids off at the school near us in theirs year round, unless the snowfall has been particularly heavy, but that is the exception instead of the rule.
I prefer against sharing my specific location but western Canada in an area where there can literally be a 60-70°c+ difference between peak winter and summer conditions.
Studded tires are magical for bikes. I feel safer biking than walking when it's getting slippery outside. Urban Arrow and other bakfiets style bikes have canopies to keep bad weather out. I didn't have a bucket bike but even then, my kids' only complaint about the weather is that we skipped the playground on the way home.
I could see this for ice but I'm thinking more snow and slush, which where can be near bumper-height on cars (not to mention the double-digit degrees below freezing for temperatures).
It's one of those things where it's probably a good idea for bigger cities with nicer weather (or better maintenance of dedicated bike lanes), but in smaller centres a better investment in public transit would make more sense