Question

water as ice has a cooling effect that water at 0degree

Answer 1

Both ice and water at 0°C cool down other bodies by extracting heat from them. However, when you supply heat to water, it's temperature rises, but in the case of ice, it first melts, and then the temperature of the formed water rises.

Therefore, even if both the ice and the water end up as water finally, the ice extracts an extra amount of heat from the body to be cooled, given by-

ΔH=Lf×M

Where Lfis the latent heat of fusion of ice, and M is the mass of ice.