if you fall through
A lot of people who fall through could climb back out before they lose too much body heat, but the wet ice is too slippery. Keep sharp objects handy (even a set of car keys can work.. but ice picks are preferred).
You've got to stay calm enough to get out quickly... that means be mentally prepared to fall through. It may help to take a "polar bear swim" on your own terms, so that any accidental winter swim you take won't be your first, and therefore some of the mental shock value will be lessened.
This time of year is perfect for a polar bear swim. There are usually charities that sponsor such events so you could help raise money for a good cause in the process... or at the very least, get yourself on TV with the other swimmers. First ask your doctor if you're in good enough shape to do this - we don't want any heart attacks!
Before you go in the water, have a hot place waiting for you. Have some hot chocolate or hot liquid Jello ready to drink so you can also warm yourself from the inside out.
Plan on being tired for a few hours, or even napping beside the wood stove (which is an amazing feeling after a polar plunge). A cold water swim does that to you. Cater to your immune system for a couple of days in case any germs made headway while your body was diverting all its energy to replace lost heat.... the usual "virus prevention steps" that everyone should take in winter anyway (rest, fluids, etc.)
If you fall through ice, you won't have time to collect your emotions. You'll need to be able to act rationally right away. You'll have only a minute or two before your muscles get too cold to do anything for you, and only slightly longer until your brain starts to cool which will affect your judgment and motor skills (hypothermia is similar to drunkenness.) You've got to make the most of the first minute, while you still have good body heat.
Another idea: Wear a life vest while on the ice. Make sure it can support your body weight plus your winter clothing.
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