Heh...the very few times I went out when there was still ice on dirt trails, I went down on each and every patch, I think. Bike went one way, I went the other.
I did NOT get good at it.
Rode to work in the spring, summer and fall in Germany, but ice and snow didn't like me. That ride was nice, though. Sembach is built on a hill, and the way to work was ALL uphill, but that was in the morning when it was cool. In the afternoon, I just had to peddle around the one-way circle at the top of the hill and coast down from there.
You can control a bike on ice as long as you don't have to turn or stop ;~D
You can get snow tires for your bike (I had 'em in college). They look like regular tires but they have little metal studs worked in with the tread.