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In my mind, ice age precedence is logical, given that "mate" is a shortcut to taking the king. If, at the end of move 20n an Ice Age occurs and means that white can no longer take the king, then the game would continue.
DarwinKoala: At first I thought that enforcing the Ice Age before evaluating the position would be too big an advantage for White because he can mate on move 20, 40, 60 in a conventional way but Black cannot. But maybe this evens out a bit that Black has a serious advantage in always having the last move before the Ice Age.