I agree with lukulus that it would be more logical when the mate would be checked (and counted) first before the Ice Age occurs, although his example isn't a proof that it's actually handled this way. As far as I can see there is no such proof in the database. I looked at all games which end with a mate after Black's 20th (40th, 60th, ...) move, but all games I've found are by direct contact with the white King or by a Knight's move (see link list below). This is not a positive proof that Ice Age occurs first, because maybe no one yet dared to try to test the behaviour ;) The other positive proof would be a game that continues after a would-be-mate after Black's 40th move, but that is hard to find in the database because in such a game the move wouldn't even be marked as a check, so one would have to go through all games with at least 41, 61, etc. moves. So we should simply wait for the one with the inside knowledge: one short post by Fencer would be enough: "Mate" or "Ice Age"? :-)

20th move
Ronin - talen314
El Cid - Pioneer54
Nuno Reis - pauloaguia

40th move
Franklin - volor
yoyudax - asdf
Jaymom - chudu1980

60th move
diogenysos - basplund
Brainwave - Jatack

P.S.: Well, after looking at all those games once more, in each of them actually an Ice Age occured although it's already mate. Maybe that's an indication that Ice Age occurs first?