This morning, I greeted the dense blanket of snow in Texas with a bike ride. The snow did not make for easy travel. Perhaps this product called reTyre might help. The company of the same name, which is based in Norway, makes snow treads that zip onto bike tires.
You start with a base tire which has half of the zipper. Then you can add one of three different treads for ice, snow, and, I think, mud.