What is the meaning of "Skating on thin ice"?

In many places, ice is as widely used as bread, and it would be surprising indeed if ice did not give birth to many special phrases.
    The expression, "to break the ice", meant, to make your first move, to do something for the first time; it was not possible until the ice was broken. Later, the expression developed another meaning, covering a relationship between people. When you have not broken the ice with someone, you have not yet cleared the. way to his trust in you, to his friendship, You must get through to him, just as the small boats had to clear the river’s ice jam.
     When you tell someone that he "cuts no ice" with you, you are making certain things clear to him — that you are not moved or impressed or influenced by him in any way. You are putting it to him straight — that he is getting nowhere with you.
     "Skating on thin ice" is something else again. This means that a man may be doing or saying some- thing risky. It might be offensive and get him into trouble. Thin ice is not much support; if he is not more careful, he may sink right through.
     In sports or any other kind of contest, you will hear the phrase, "The game is on ice" or "It is iced up". This simply means that the game is really over, that one side is so far ahead that the other cannot catch up. There is no longer any doubt as who the winner will be.