A scary experience if it happens for real I'm sure, but I guess like most things preparation can definitely help! When Royal Marines go to Norway for the first time they all undertake whats called the NSSC (Novice Ski / Survival Course), part of the course being Ice Breaking Drills. It's quite a simple drill really. A hole is made in the ice by one of the instructors using a chainsaw and the students line up next to it. The same set of skis are used for everyone, string attached to the ends to get them out afterwards. One by one the students go in, first thing required when in the water is "don't panic!!" Of course it's cold but it's still only water, any colder it would be ice!! Then recital of your name, rank and number, followed by kicking off the skis and shouldering the bergan off your back onto the side of the ice. Then its a matter of using the ski poles (which you don't want to let go of!) as ice picks and clawing your way out of the hole. The instructors normally give you a tot of rum and you might toast the Queen or suchlike, you then roll in the snow for a few seconds (as mentioned in BOD's post above) and then it's a matter of getting out of the windchill, and into a dry set of clothes (especially socks!) or within a few minutes obviously you are going to start to freeze. Its standard that everyone carries a big flask of hot drink with them during the day which would have been prepared that morning so now is the time to get drinking and get warm from the inside as well! From a tactical point of view, fires to dry clothes are probably going to be out, so this comes to the other very important point also made above (dommyracer) about always having your spare clothing and equipment well waterproofed.
It's a drill that a lot of Marines enjoy, and it definitely adds to your self confidence and confidence in your colleagues, a good thing in the Arctic I think!
It is certainly an experience that you never forget! I always carry the photos of me doing the Ice breaking drills when I go out in winter, and when I get a little bit chilly or my mates say their a bit cold I look at them or show my mates and we soon realise that we are not actually that cold!
Its one of my life experiences that I am glad to have done, for that just in case situation and I agree with SunDog that it definately adds to your self confidence.