If they plough well where you are, get winter tires for the bicycle. They are magical. For clothes, use double gloves and pull over pants. I can guarantee this down to less than -20C.

Caveats: Good winter tires are expensive, the magic isn't the spikes but the rubber. Be careful when you step off the bicycle, you have no clue how slippery it is. After bicycling a while with winter tires you can't bicycle without them, you lose all reflexes for handling slippery ice.