So I just tried riding my new Bianchi Axis in sloppy conditions for the first time this morning. I went out for a run while it was still dark out and by the time I got back it was snowing hard and had dropped four degrees. I packed my commute backpack, changed into bike clothes and headed out. By this time two inches of snow had accumulated and started to pack in the morning rush traffic. About a block from my house, a line of cars stopped abruptly at a green (someone must have been pulling out further down the street). I grabbed a handful of brake and my bike slid right out from under me on a patch of ice. Luckily no cars behind me... I think I'll have a nice bruise on my hip tonight (hurts a little to walk), but that's about it, and the pretty new bike has didn't get even one scratch, just scuffed up one corner of bar tape (I cushioned its fall I guess) -- but I realized I really have no idea how to handle my bike in this kind of weather. I sheepishly walked my bike a block back home, showered and drove in (witnessed a few car accidents on the way, making me feel slightly less defeated).

So can anyone give me tips for handling, braking, etc (basically for not crashing) in slippery conditions? Also tire tips? I currently have the tires that came on the bike - since it's a cross, they're fairly knobby 700x35s running a fairly low psi.

I really want to ride this winter...