Way back in 1981 I heard that road racers ride fixed gear in the winter for conditioning. I built a fixed gear bike for myself. It taught me how to spin fast, and surprisingly, it taught me how to climb better since I couldn't shift down. Another surprise was that it seemed to keep me warmer since I was active for a bigger fraction of the time.
These days I appreciate fenders more than ever, so maybe I'll put a pair on my fixie for the winter. I have a much shorter commute than I've had in many years, and it's not hilly, so taking the fixed gear isn't a big undertaking.
The bike I ride the most has 20 gears and fenders, and I'll ride it in nearly any outdoor conditions.
On really bad days where there is slush or ice and there is also salt, if I do choose to ride, I'll probably take Citi Bike. Those bikes have drum brakes and wide tires, and I don't care about damage to the bikes.
(stock photo)