Please send a note to the Dutch (and the Germans, the Danish, the French, the Belgians, …) to tell them to stop riding their bicycles in the midst of winter.
In the past five years there was one day when I couldn't cycle to work due to black ice covering most of the roads, and even that resolved itself in the afternoon. Snow just means you need a bit more dexterity than usual.
As for comfort; proper clothing means you are pretty much comfortable most of the time.
The ultimate irony of the point attempted to be made is that people don't drive when ice or snow cover on the road (or suck at it, take undue risks, fail to, and ram into curbs/cars/people).
Many people don't though (look at how attendance rates plummet at schools and businesses on heavy snow days), and of those who do drive anyway, the accident rate is highly elevated.
I cannot relate to what you write at all. In all my years in school, I did not witness a single day of attendance drop due to weather (the only weather-related exception was for the early years of elementary school, when you could choose not to go outside during breaks if the temperature was low enough, but that was rarely the case here near the coast).
What's more, in bad weather people (who have the option to choose between public transportation and their own vehicles) tend to choose cars more often because public transit has a habit of becoming increasingly unreliable, especially due to winter conditions, even though such conditions can be reasonably expected for 6 months a year.
I grew in a mountain pass area where there (used to, times change...) be heavy snow 2 to 4 months per year, and learned to drive there. Now I live in a city where snow happens regularly but much less and typically goes away in a couple of days, and when there's snow there's much less people on the roads, and for those who are, only a fraction know how to handle it, or even have proper winter tyres even though temperatures dive below the freezing point every year. People routinely flat out skip work on such days because "snow", which coming from where I grew up, is unfathomable unless you got a meter of snow overnight. On the occasional trip to Paris I've witnessed a couple events where emergency services are scrambling to bring water, food, and clothes to people gridlocked for hours (it was winter and many couldn't be arsed to take even a jacket, oblivious to their environment, living in their air-conditioned bubbles from house to covered parking lot to car to workplace); the entirety of the city streets was in deadlock because of a couple of millimetres of snow (obviously {rail,sub}way was unaffected). Pure madness.
Where are you from? Where I'm from, schools would be closed during heavy snowfall, so attendance would necessarily drop to zero. That's kind of necessary in a place where snowfall doesn't happen often enough for it to make sense to invest in a whole fleet of snow-clearing vehicles. It would take days to clear the streets from a heavy snowfall, but snowfalls like that happened less than once a year.
A few years back I took a trip to Sapporo over the New Year's holiday. It snowed ~3 inches per day the entire week I was there. I consider myself pretty comfortable with cold weather (I went up there so the girl I knew could teach me to snowboard). I'll be damned if I ever agree to give up a private auto in favor of biking in that sort of weather. I didn't even like her FWD Kei car, and wished I was in an AWD Lancer Evolution or Subaru WRX instead.
I live in the southwest of Germany, 500km from the coast as the crow flies. I cycle-commute year-round, around 5km each way. It's no problem if you have a good rain jacket and rain pants, and a down jacket, gloves and a hat (that fits below a helmet) against the cold in winter.
In the past five years there was one day when I couldn't cycle to work due to black ice covering most of the roads, and even that resolved itself in the afternoon. Snow just means you need a bit more dexterity than usual.
As for comfort; proper clothing means you are pretty much comfortable most of the time.