Then, why is ice so cold? It is because ice requires heat when it melts to become water.
Heat is necessary for ice to melt. Ice does not melt when it is cold, but it does when you put snow on the palm of your hand. This is evidence that when snow ice melts, it gets heat from somewhere.
The source is, of course, your hand. The snow melts using the heat from our hands. This is why we feel a cold sensation when we put ice on the palm of our hand.
The heat required for the melting of ice is called heat of fusion. When snow melts, it feels cold because your hand is deprived of the heat of melting.