It seems to stop at least a number of them, even in places like Denmark. Look at the answers to this question, "Do Danes ride a bike in heavy rain?"[1]:
> Yes, though fewer will than in nice weather.
> Bus fill up more then usual in rain, though
Or this blogpost about people from Copenhagen biking through the winter[2]:
> As mentioned before, 80% of Copenhageners cycle through the winter. That number is surely lower when we have hard winters with snowstorm after snowstorm, but the numbers are still impressive.
And keep in mind the number we'd be interested in would be lower - not just how many people generally cycle throughout the winter (which seems to be ~80%), but how many of that 80% still choose to cycle on particularly cold or snowy winter days.
So even if we could have infrastructure on par with Copenhagen, and even if we get a corresponding cultural shift (neither of these are easy or quick tasks), we would still need the other forms of transportation infrastructure to be able to handle the spillover that occurs when large amount of bikers don't feel like biking.
[1] https://www.quora.com/Do-Danes-ride-a-bike-in-heavy-rain [2] http://www.copenhagenize.com/2011/01/cycling-in-winter-in-co...
> we would still need the other forms of transportation infrastructure to be able to handle the spillover that occurs when large amount of bikers don't feel like biking.
Not necessarily. If you don't have (enough of) that infrastructure, less people will be tempted by it. I imagine the 20% in Copenhagen switch to public transportation because it is well developed and convenient. When I commuted by bicycle, weather wasn't a factor because I had no convenient alternative. Ditto for my colleagues who commuted by bicycle.
I agree that the biggest problem is cultural.
If you somehow get people to try, they also discover that biking in really bad conditions is actually quite a lot of fun, provided you are wearing the right clothes. In the cold, your usual jacket is almost always enough because you're exercising anyway, but you'll need the best gloves and hat you can find. The days where I got to work in a snowstorm are actually my most productive :)
The real problem in bad weather conditions is that the threat from cars is amplified: it's usually dark in winter, snow and rain further deteriorate visibility, and snow/ice are dangerous because both bikes and cars are less predictable. Bikes are also extremely vulnerable to blocks of hardened snow that often get shoved right onto their usual path by cars.
Why do you "have to" build more car infrastructure? If traffic gets worse when the weather gets bad then there's even more incentive to bicycle despite the weather. That's the whole point of cycle-first, transit-first, pedestrian-first city planning: Cars don't scale, so stop trying.
A lot of bikers won't bike when the weather reaches a certain point (too cold, too much rain). This means that even if you build infrastructure for bikes, you're still going to have to build just as much throughput for other modes of transportation as you did before (they have to handle situations where no one is biking).