Also we don't get slush; I did when I lived 700 miles south of here but everything up here is fluffy. I will say this, a bicycle wouldn't cut it. :D It's either a 4x4, a snow mobile, or you stay home.
I've got a mountain bike, which means massive grip on snow and good even on slush. The gears still get clogged up, though, so if it's slushly, I pretty much have to choose a gear ratio and then stick with it unless I feel like fishing through them looking for one that works.
Also, I presume you've never heard of fatbikes.