I spend a lot of time on the ice working and playing each winter.
I have extracted myself after falling through the ice a few times, both in training and for real.
Ice picks make it much easier to get out of the hole onto solid ice. I carry a commercial set of quick-release ones around my neck whenever I am snowmobiling across the ice. Be sure to get the picks that float (some don't) and that have long points (about 2 inches) as the short tipped ones do not dig into punky ice well.
I often see sledders with the picks mounted on their snowmobile, but I wear mine so I know that when I fall through they will be with me.
When we were kids we used to carry large spike nails in out pockets to do the same task.
I also keep a rope throw-bag around the handle-bars of my snowmobile to rescue other people when they go through the ice.
Mike.