We've only had one day this winter with scary glare ice, but I rode my brakeless commuter fixie and felt very confident. As confident as you can feel on glare ice anyway. Brake or no brake, gravity is going to have it's way with you if your front wheel loses traction. A front brake turns a bike into a sled on ice, so even when I had one I didn't use it much in the winter. Two good things: Chicago keeps the main streets very clean, so you should never really have to worry about ice if you stick to 'em. Second, I've found that wide handlebars give me better winter control when I do hit something slippery.
The other night I was trackstanding in the snow outside of the liquor store, spinning my wheels and bunny hopping around while my friends bought beer. Then I fell completely on my ass, snow all over the place, still clipped in, bike sticking in the air, looking very foolish. This went over quite well with the pedestrian traffic, who like nothing more than to see some cocky cyclist fall down. I was in a pretty good mood though, and a couple of girls even smiled at me as I lay there.