Aside from the days when there was snow/ice, I rode all through last winter. I used a polar buff under my helmet to keep my head/ears toasty, and on the days it was really cold, made it into a balacava to cover my face/neck. Usually three layers for my core: Craft thermal shirt, then jersey, then jacket. To keep my hands warm, chemical hand warmers and Amfib lobster-style gloves. Tights w/chamois and on particularly cold days, I'd layer leg warmers under them. Wool socks, chemical foot warmer, toe covers and good quality booties/shoe covers for my feet. The worst part of winter riding is cold hands/feet.
I would never ever ride if the roads/trails had enough ice/snow that it was hard to get around the slippery patches safely. It's not worth risking injury and possibly months off the bike.