I've taken some very dangerous falls on black ice in the past, so nowadays during the winter I use studded tires - schwalbe marathon winter tires.

I also have fender with mudflaps which help keep the crud off.

I have platform pedals so I can wear winter boots with thick socks. Balaclava under my helmet. When it is really cold I will wear knit mittens with nylon over-mitts. Mostly I find it's hands and feet that need to be bundled up good. I wear Sport Hill knit pants that are made for cross country skiers.