I'm in this ame delima as you right now. This is my first year of consistantly commuting to school. I live in Chicago about 3 miles east of Lake Michigan my school is on Michigan ave. which is one block west of my street Indiana Avenue, but 5 1/2 miles north. The further north you go the farther west the lake comes so my school is just over a mile west of the lake.
Anyway I just bought a new bicycle this summer. A Specialized Crossroads Sport hybrid. It is actually meant for people who are old and fat but I like it even though I'm 15 @ 140 pounds. I have done a few things to it though to make it more suitable for me (thinner less cushy seat, slicks, and some nice toe straps. Plus a rear rack and panniers.
I am currently trying to decide what kind of tires to get. I tried snow riding once last year on a road bike . I would go up the sidewalk but it was hard to keep traction in all that snow. I would start on our part of the sidewalk which was shoveled and get up to speed. Once I got to parts of the block where it wasn't shoved my wheels slipped alot and I was brought to a slow stop. My wheels had no traction whatsoever.
My current commute uses about 3 blocks of unplowed streets but the rest is plowed. I think the 106's will do fine for me but not sure.