A Clarification on Ice Age Chess Rules

This came up in at least one game on Brainking. In this position (first diagram) Black is to make his/her 20th move. Black can move 20... Qf3+ which would have been checkmate except that right after Black's move, the Ice Age event happens and ice cubes are placed on the board. This prevents the mate from taking place, the game continues, white to play (see diagram 2).



The argument here was that once checkmate happens the game should end right at that point. However, the way I see it, the Ice Age event is an essential part of the game and should the Ice Age happen next turn, White can consider that as a part of his/her defensive plan.

This (being able to use a coming Ice Age as a defense) probably gives White a slight advantage, however this should be balanced with the fact that black makes the last move before the Ice Age, hence has a slight advantage as well.

Note: The position here is not from an actual game.