Why is fresh ice sticky?
Whether or not the ice cube will adhere to something is dependent on the temperature of the ice, the state of the surface of the ice, and the moisture content of the material. 

The temperature of an ice cube can range from the freezing point of water ($0\ \mathrm{^\circ C}$) to well below this temperature. Typically most materials have a small degree of moisture regardless of whether they are “wet” or not. If the ice cube is cold enough, it will freeze the water present in the material. The giant covalent network structure of the ice extends into the material, accounting for why it sticks to the ice—the moisture in the material has become part of the ice cube.

If the surface of the ice cube is has melted, it will not be able to freeze the water in the material any more than it will be able to freeze the ice already melted on its surface. No giant covalent network solid will form, and the ice will not stick to the material.