Saved By His Socks
Being immersed in very cold water without protective clothing feels like being in a vice. Some people are more inventive than others in this situation. I recently spoke with woman in Errol New Hampshire who told me a locally well known tale involving her father who was snowmobiling alone on one of the many local ponds. His sled broke through. The ice he kept breaking as he tried to get out. At some point he removed his shoes and socks (presumably to be able to swim better). Things were starting to look really bad. Fortunately by then, his socks had frozen to ice enough to the ice to give him enough grip to get himself out. He made it back to his truck and survived.
Someone called rescue at some point. They arrived after the victim had gotten out and headed for his truck. Not finding the victim, they called in divers. He was declared missing and likely dead. It was a very happy reunion when he showed up at home.
He was both tough and more comfortable than most in cold water. When they fished his sled out, rather than hiring a diver, he stripped to his skivvies and jumped in with a rope and tied it to the machine.
The woman said the day of the accident was cold which, in the Great North Woods, usually means 10 degrees or less. Letting wet coat sleeves (or socks in this case) freeze to the ice has worked successfully in a number of situations at these temperatures. I am not aware of it working well in temperatures nearer to freezing. Even in cold conditions, there is a big range in what grips well. Things that are fibrous and wet well (cotton for example) adhere to the ice much better than smooth water resistant nylon. As for using your socks, when you are fighting for your life, anything that works is good. Ice claws would be a lot faster and more effective than socks or sleeves or just about anything else other than a throw rope from a friend.