kleineme: I'd be much more inclined to ask the game's inventor (or leading players, if the inventor is not available), rather than basing anything on the actual implementation here at BK.  There are things here that could stand improvement.

I'm a variant lover but not an ice age player, so feel free to discount my opinion.  But I'd much rather see the rules of what constitutes "mate" remaining consistent throughout the game, no matter what the current move number happens to be.  Let a move be completed before an ice age occurs.

The "taking the king" argument leads one astray.  If you follow that "logic", a king could move into some checks, secure in the knowledge that an ice age was about to save him.  I'm sure we don't want that.