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...