>>49320661better idea: make ice resist fighting or at least make it neutral.
it makes sense that Ice beats fighting because "punch break hard thing" like it does with rock and steel but you can make a case for the reverse too. intense cold saps your energy and makes it harder to be active as your body is focused more on keeping you warm, shivering, getting stiff, etc.
granted the normal interaction still works and counterpoints to my idea is that someone well- trained enough could ignore it, or that physical activity helps keep you warm (which might actually be another reason fighting is SE now that i think about it), but if someone's gonna turn one of ice's weaknesses into something else then it makes more sense than something as counter-intuitive as fire.