When I moved to college in Idaho as a teenager, I had a really quick introduction into a new world of snow and ice. While the snow I grew up with was wet and heavy, and usually melted away pretty quick in the moderate temperature. Idaho however introduced me to the bitter hard-freeze that left our campus with an amazing array of forms of ice that were completely new to me. I, as with many of my fellow students, became intimately familiar with this ice while performing the splits, or landing on my back when trying to hurry between classes.
In that time, I saw a few people that had some nifty attachments for their shoes allowing them to get traction on the ice. Along the lines of higher end crampons used in ice-climbing, they strapped on over any shoes and allowed the user to dig into the ice a bit more. Over on one of my favorite sites (Instructables) there are some instructions for creating a simple version of these yourself.