I agree, winter SUCKS!!!
One of the bike shops in my home town use to put on winter "ice" crits. It was a blast and helped the riders get through the winter time. All you need is a mountain bike and a set of studded tires. I think you can buy them for ~$40-50.
You can make your own a lot cheaper than that if you want. If you've got a set of knobbies laying around (preferrably a set that you proabably aren't going to use again) just mark a pattern on the tread for the studs, go down to your local hardware store and buy some 1/2 inch screws and nuts. Drill the screws through the tire where you marked your pattern, screw the nut on (you may want to use some lock-tight). Then, MOST IMPORTANTLY, cover the screw head on the inside of the tire to prevent flats.
To do this, find a pair of old tubes laying around (you may be able to talk your bike shop into giving you a set that have holes in them) cut out the valve stem, then make a cut that runs the entire inside of the tube (make sure its the inside and not the outside... the outside of the tube is what will protect your inflated tube from puntures). Wrap this tube around the inflated tube and mount as you would a regular tire.
If you don't have a spair tube laying around you can use duct-tape: apply about 1 square inch of tape over the head of the screw (this method won't last as long as the tube method, but it should still help prevent the screw from tearing into your tube.)
BAMMM!!! you've got yourself a set of studs!

Now ya just gotta find a bike shop or a group of friends to race against!
P.S.
If you're having a hard time finding a parking lot with snow and ice... bring a bunch of water to dump in the turns, wait about 30 minutes and let the fun begin!
P.S.S.
As fun as it is, it may result in injury or possible death! WEAR A HELMET!
