Hi Katie,
Wow, I hope you pack a spare change of underwear in your survival kit, because that's the first thing I would need after punching my snowmobile through the ice.
It is very freaky when it happens but both times I got out of the water very quickly. My employer provides mandatory Ice Safety training/equipment; full floater suits and long ice picks really help in getting out of the water.
Another time the rear of the snowmobile and I went through a beaver pond but the front of the machine stayed up on the thin, mushy ice. Every time we tried to pull on the front of the machine our boots would break through so we cut conifer limbs and built a platform around the 1/2 submerged snowmoblie. It was a very light Ski-doo Elan model and my magnesium snowshoes were tied to the rear handgrip. By squatting down at the rear of the hole and sticking my arms into the water up to my shoulders I was able to get a hold of my snowshoes and lift the rear up to the point where my partner at the front and I could roll the snowmobile sideways to shore. We broke the windshield and cracked the cowling but the snowmobile still ran and I drove it out to the truck. I was almost completely wet and my partner was wet to the waist so we called it a day and headed to town.
This was long before the days of being prepared, I now keep a full change of clothes (including underwear) in the work truck or my personal outdoor vehicle. Usually they end up being used for an unplanned stay at a motel in another town, but I and others have used them after a soaking in the bush.
Later,
Mike