Water at 273 K is less effective in cooling than ice at the same temperature. It is because :

Water at 273 K (0°C) is less effective in cooling than ice at the same temperature because water at this stage possesses more internal energy. When ice at 273 K melts into water, it must absorb a significant amount of energy known as the latent heat of fusion [1]. Specifically, it takes approximately 334 joules of energy to convert just one gram of ice at 0°C into liquid water at 0°C. Consequently, water at 273 K already contains this additional latent heat that ice does not. When ice is used as a cooling agent, it absorbs this extra energy from its surroundings to undergo the phase change, thereby removing more heat from the environment than water at the same temperature would [2]. Therefore, the higher energy content of water at 273 K makes it a less efficient coolant compared to ice.

Sources

1. [1] Physical Geography by PMF IAS, Manjunath Thamminidi, PMF IAS (1st ed.) > Chapter 22: Vertical Distribution of Temperature > Latent Heat > p. 294
2. [2] https://www.britannica.com/science/latent-heat