Breaking through ice into water is an extremely dangerous accident, possibly even aggravated when it happens to people on skis or snow shoes, as these load-distributing attachments allow people to travel far out on ice that’s too weak to withstand greater load concentrations, for example people standing in boots: rescue efforts inevitably cause greater pressures on the ice near a break-through, with the increased chance of rescuers breaking through as well.
For these reasons, all possible precautions should be taken to prevent an ice break-through accident:
The suggestion of carrying and using an ice auger to directly measure the ice thickness may sound laughable in advance, but would undoubtedly seem a lot more sensible to survivors of such an accident. Is your route known as a typical crossing point? If not, consider possible reasons. Is it known to be a safe route? Is there any sign of other people crossing recently? Has the weather been consistently cold for some time up to your trip? Has there been warm weather recently or at present? Water on the ice, especially near shore, indicates melting and weaker ice. Any open water should be cause for reconsideration.
In spite of an earlier comment, the use of skis or snowshoes is advisable for crossing ice, as they distribute your weight and may prevent breaking through if you cross a thin patch. Fortunately, mountaineers almost invariably use skis or snow shoes for winter travel.
A party crossing ice should spread out to avoid pressure points on the ice.
All ropes should be carried so they are immediately accessible.
The heaviest person should not carry the rope, and should not go first, but rather be centred in the group or farther back, as the first or heaviest person is the most likely to break through.
Once in ice-cold water, a victim needs to get out of it as quickly as possible to improve his chance of survival.
He should first of all try to get his rope (if any) to his party still up on the ice, though obviously they should keep back from the broken edge, and keep away from each other.
Next, he should shed all his obvious encumbrances, including pack and skis or snow shoes, and best if he can save them by getting them back on the ice, but a minimum of time and effort should be spent on saving equipment if there’s any difficulty: the priority should be to get the person out of the water.
The victim(s) should get back to the ice in the direction from which the party approached.
Meanwhile, ideally his party have been setting up any sort of anchor and getting a rope ready to help him to get up on the ice there, as a long rope pulled by team members should be most expedient to get a victim up on the ice.
Otherwise (no rope available), the use of ice axes has been suggested and would likely be very effective, but rarely available. This is something to think about: undoubtedly any ice axes and screws should also be carried readily accessible when crossing a lake.
A technique has been demonstrated, of swimming by kicking the legs while supporting the body with the arms on the ice and squirming to get up on it; then roll and crawl well back from the ice edge. Here is a helpful video.
As well as making every possible effort to avoid this kind of emergency from the start, the advantages of having team support, pre-planning, and preparation are obvious:
An ice-crossing party should use skis or snow shoes.
They should spread out while traveling on a lake.
Ropes, axes, and ice screws should be distributed among the party while traveling, and kept accessible.
The heaviest person should not lead the way, and should not carry ‘the rope’: he may carry it once shore is reached.