I usually just use the "stay straight and no sudden movements" technique for wooden bridges (and patches of snow/ice) but I heard my wife say something behind me and when I turned I went down. I don't use studded tires, just vittoria 37mm ones. I'd like to go up to 40mm soon....
I actually like tires with some type of tread pattern, even a subtle one. I have read Sheldon's and other sites about this, but just can't agree with them. Every time I've used a smooth tire I bite it more around wet corners, leaves, and bridges.