When I was in College we did a day of 'Ice safety' up around Gravenhurst. We had on dry suits and practiced getting out of the ice using picks, bars and nothing.
A few of us mentioned to our prof 'This is all well and good, but if we go in it's not going to be with a dry suit on' so after a bit of persuasion and complete supervision he agreed to let us jump in with just our clothes on and with zero assistance.
When it was my turn, as soon as I hit the water, I felt the energy drain from my entire body, like I had just finished a 2 hour workout at the gym. Even keeping my head afloat was difficult. I kept trying to kick and beach myself up on the ice but to no avail. Finally, I saw a chunk of ice that had frozen on top of the other ice at the edge of the hole we had made. I was able to grab it like a rock climbing grip, and roll myself onto the ice.
Needless to say, after seeing how tough saving yourself can be, I'll never go on the ice without a float coat.