In Version 3.62, I went fishing on a freshly frozen lake. I could not walk there on the wilderness map, but was allowed to crawl. The ice was not so thick, it took 6 minutes to make a hole with a javelin. It also made a cracking sound when I got up and walked on the ice.
So what happened was that at some point, i dropped a pike on the ice. The game made a splashing sound and rendered a water hole graphic below my character. The strange thing was that I was still standing. I only fell into the water (same tile) when I tried to walk away. On a second occasion, the same thing happened when I dropped some branches on the ice. That time, I did not walk away. Instead, I went prone again and in that case the game allowed me to get to the next tile without getting wet and cold at all.
I am not entirely sure why the ice can support a 80kg person standing on it while breaking when I drop some weight I was carrying all along, but maybe this is intended. But once the ice breaks, the player character's status needs to be updated before the next turn. This should be straightforward to reproduce, but I can happily provide a savegame if needed.
Cheers!