We had a place on a lake where two areas about 100 feet in dia. usually didn't freeze in the winter because of springs but did freeze when it was exceptionally cold. So I would suspect there are many lakes with thin sections because of springs.

When I was a kid we had a creek not deep enough to drown in that ran through our town and we could ice skate from one side of town to the other. While skating one foot broke through the ice and tangled through a tree root. I couldn't get my foot out and finally had to reach underwater to unlace my skate to escape. A little scary at the time.