Question

How is water at 0 o C has greater Energy than Ice at the same temperature?

Answer 1

The one that absorbs more heat from you will cool you more, and seem colder. But it isn't entirely straightforward.

If you pour water in your hand, water will flow to fit you. An ice cube will not make as good contact.

Water in contact with you will warm. It can then flow away and be replaced by fresh cold water. Ice doesn't flow

On the other hand, Ice at freezing will melt. This takes energy and leaves you with water at freezing.

Another point is that water is slightly denser than water. So for the same contact patch slightly more water is in contact with you than ice.

You are more likely to freeze to death in a rainstorm just above freezing than a snowstorm just below freezing. The rainstorm will soak your clothes and keep them from insulating. The snowstorm will leave you dry.

Edit - Latent heat of fusion

As suggested by Floris. See this Wikipedia article for more information.

Temperature is a measure of kinetic energy per molecule.

Water is a polar molecule. The H atoms in water have a slight positive charge, and the O atoms a negative charge. At low energy, this attraction gives rise to weak bonds, and ice forms.

As you raise the temperature, molecules vibrate harder. At a certain point (the melting temperature), vibrations are violent enough to begin breaking bonds. At this point, the temperature cannot rise. That is, if you add energy, the kinetic energy of the water molecules does not increase. Instead, you break more bonds, and this absorbs the extra energy.

When all the bonds are broken and all the the ice has melted, added energy once again goes into increasing the kinetic energy of water molecules.

It takes about 335 Joules to rupture all the bonds in 1 gram of ice. So the specific heat of fusion of ice is 335 J/g.

The latent heat of fusion is the amount of energy needed to rupture the bonds in whatever amount of ice you have on hand.

Since you are hotter than the ice, your molecules are have more energy than those in the ice. When you touch ice, your molecules bump into ice molecules and add energy to the ice. You lose energy and become cooler. Energy keeps flowing from you to the ice until the temperatures are equal. Thus it is important that melting ice is not warming as you cool.