Biking can be a pain sometimes.... it can even be more of a hassle in zero degree weather riding on a sheet of ice.
One solution, is to purchase brand new expensive snow tires to help with you daily commute. OR you can go the cheaper direction and do what Fritz Rice of Dutch Bike Co. did by using Zip Ties...!
I can accelerate, brake, and corner with aplomb, even on the vile snowpack/sheet ice mix the plows leave in the bike lanes. The zip ties dig nicely into the hardest packed surfaces, but they're thin enough not to bounce the bike around at low speed or on short pavement sections.