It is very easy to walk carefully on ice and not fall, with non specialized shoes. Not sure where you're getting your info, LOL.
That's the key thing, though. If you *walk* across the ice, you won't slip and fall. If you click far enough out that you *run* across the ice, you will fall. See?
No, *you* see it now that it was pointed out to you above, but no, it still doesn't make sense, because the gold standard in this game is "characters path around obstacles" i.e. act safely, and in this situation they run across. And you don't have a way to enter walk mode aside from clicking a few feet in front of you. That is a failure of interface, not "aha you carelessly ran across ice". You're grasping at straws and it really shows. But hey, why bother responding to internet comments.