I cycled to work for 3 years in Paris. Cycling on fresh snow isn't so dangerous, but on ice it is as you won't be able to brake. Also, cycling by -20°c is a very uncomfortable experience and increases a lot your chances to die if you fall and pass out.

Last, cycling, especially in winter, is good if you're able-bodied, but it leaves out people with disabilities, which makes a sizable amount of the population if you take aged people in the mix.

I agree with OP that in general, a good public transportation system is the first step toward better cities with less cars. Bikes can play a role, but can't be the solution for everything.