Question

why is ice at 273 K more effective in cooling than water at the same temperature

Answer 1

This is because of the fact that phase transition occurs at same temperature.  

Answer 2

Ice at 273°K or 0°C is more effective in cooling than water at the same temperature, due to the fact that for melting each kg of ice latent heat required is of 3.34×10^5 Joules fron the substance and hence cools the substance more effectively.