Today I rode my bike to work in a few inches of snow and "feels like" -13C (9 degrees F). I only almost fell over twice.
But I was not the only one riding my bike to work! That's something I love about Finns - they are hard-core cyclists. Here is a picture of the bike rack outside my work at the end of the day (it was even fuller during the day).
There is such a thing as studded tires for your bike, and even snow tires (they are very fat). I might look into the former before things get too crazy out there.