They can be a great relief during the bad breakouts and particularly soothing for acne and inflammatory skin. A nice touch for using ice cubes would be to freeze your favorite fruit and vegetable juices into ice cubes. That would provide your skin with immediate anti-oxidants and the various benefits which come from topical application of the particular fruits.
The essentials would be orange juice which is useful for bright face and apple juice which is great for oily skin. You can also go for pomegranates as they are especially high in anti-oxidants and would provide a rosy complexion.
Caution: Applying ice cubes straight to your skin can cause delicate capillaries under your skin to break so wrap the ice cubes in a wash cloth and then apply them to your skin.