I ride year around in Madison and i have 2 bikes

-Marin 29er Hardtail mountain bike for the winter and mountain biking during the summer. Complete with disc brakes, spiked tires and fenders.

-Trek 7.5 FX, this is my main bike for trail and occasional road riding depending on weather.

I highly recommend a separate bike for the winter. IMO a mountain bike equipped with spiked tires and fenders is perfect. The disc brakes come in handy but you can get buy without them.

I also recommend having access to a hose and buying a leaf blower for rinsing off and dry after wet rides in the winter. Assume anytime you bike gets wet in the winter that it has salt on it and rinse off regularly.

If you ride in the winter, be sure to bike across the lakes (assuming we get a normal winter, last winter i only went across twice)