Again from my ice safety course, The instructor told us that it can take hours to get hypothermic from immersion in ice-cold water. What gets people is the shock to the system that leads to shallow breathing, panic and loss of consciousness. In fact, one recommendation given when self-extraction from the ice is impossible is to extend your wet sleeves onto the ice surface so that they freeze in place to hold you out of the water after you've lost consciousness.
Most people that die in this situation drown before hypothermia sets in. The recommendation from the course was to take the first two minutes of immersion to allow the shock to pass before calmly initiating self-extrication. You then have 10 or so minutes before passing out. He even did a real-life demonstration (wearing a dry suit full of holes).
Part of the course was a viewing of some videos of "Professor Popsicle", a guy who studies hypothermia, often using himself as a guinea pig. The videos are available online at:
http://outside.away.com/outside/features/200212/200212_popsicle_splash.html#