Well I am retired and don't commute anymore but since I have no car it is the bike all the way just like the rest of the year. I have the advantage now in that I can pick and choose when I ride. If it's too nasty, I stay home and wait until the ice and snow get cleared. Likewise I don't need to ride when the temperature is sub zero or when there is a terrible wind. The last time I rode a bus was nearly 2 years ago when they have a free fare on the first Monday of the month and that was to go to the supermarket that's nearly a 7 mile bike ride for me.
But I walk when I cannot bike because cycling in winter conditions can be flat out dangerous especially when it puts you flat out on the road. I bought some pull-on studs for walking on ice which are great for giving you confidence when walking on ice because being an old duffer now I am concerned about falling and breaking something like a hip which could end my biking days altogether and put me in a nursing home. No thanks.
But the big upside to having no car in the winter is that I don't need to worry if it will start, or to go out and clear it off to move it when the snow plows come, or to worry about getting stuck or somebody else just sliding into me and there's nothing I can do but watch. I can honestly say I don't miss having a car at all.