Not so much for their attacks as it is just to exist. This would be why many ice-types, particularly those that have the ability Snow Warning, seem to emit auras of cold around themselves as well. A constant barrage of heat, such as from fire, can therefore easily overwhelm an ice-type because it’s difficult to process that much energy at once.
(Also, I stand corrected by my last post. Only fire is this sort of a problem for ice-types. Steel and rock fall under the same category as fighting.)