Sure, if you live in Moscow/Anchorage/Montreal/Stockholm/etc, it's miserable for a few months, but the rest of the time, you can cycle.
Plus, cycling in the cold wakes you up even faster than cycling in the heat.
I'm from Sweden, and when I lived in Gothenburg I had no issues biking in -10 - -20C or so (which is what it maxes out at in that area, and even then only for a few weeks at most).
Snow is fine to go on - the worst is like 0C when its been melting and freezing so you get slippery ice, but even then you do fine most of the time as at least the car parts of the roads tend to be maintained with gravel. Assuming you live somewhere that regularly has cold weather your roads are most likely decently graveled too.
They have the crazy huge tires as well to go over snow/ice. Each one said its not a huge deal to bike in -20ish weather with snow/ice. Just means you travel slower was their statement.