A cooler is a card that hits the turn or river that reduces your equity in the hand, like flopping a low flush only to have a four flush hit the board. Or 4 to a straight and you hold a set.
No, a cooler is anyhand you're not getting away from that you lose. KK vs AA pre is a cooler. Set under set is a cooler. If he had raised properly pre then bet/called the flop it would easily be a cooler.