Ice cools down the water. Nobody can argue that. That water is what the smoke travels through. The walls of the bubbles containing water is where the heat transfer takes place. Colder water makes the smoke colder. Another way to make smoke cooler is increase the surface area of the smoke to water (i.e. make the bubbles smaller). Percolators and diffusers are both methods of doing such.
Ice in the bong (i.e. one with an ice catcher) cools the smoke as it passes over it like how a hair dryer heats the air when it passes over a heating elemnt... just the reverse. Colder smoke burns less and makes for a better hit.