Ice - no problem. Braking on ice - problem.
A few years ago I was in the woods in the winter. Came to a big stretch of ice (a small pond). Went across, no problem. Came back across, and thought "What would happen it I hit the brakes?". Bam! I just laid there laughing, thinking to myself, "You stupid $*#&!!"
I really need to get back out on my mtn bike this winter. Also, I usually hit the deck about once each winter on my road bike. The extra clothes are appreciated.