I've driven a bicycle in winter and yeah nah, I'd rather just take public transport. It's not just traction but the fact everyone else got shitty traction too, so there is a good chance than most of the agility of small bike/bicycle is negated by just slipping.
At least with bicycle like 95% of my route is not on actual road sharing it with cars, can't do that on bike.
Don't knock it till you try it. Though be careful for the first time if you do try it, use common sense — drive slower and don't turn as sharply, dress appropriately as you'll be caked in mud. But otherwise it's doable and quite fun.