But there is good news! You can turn an old (or new) bike tire into a set of Tyre Socks which will give you more traction. Mountain bike tires would be best for mud and water while snow tires would be best for ice and snow.
(More details: Instructables.com)
Another modification idea/approach: Attach Snow Spikes
(source: Fly Jumper Forum)
Spikes from http://www.icespike.com