An ice cube melts faster in water than it does in air, given equal circumstances. Heat-energy is needed in order for an ice cube to melt. Heat-energy travels faster through water than it does through air.
The reason heat-energy travels faster through water is that water's molecules are more compact, which allows for more contact with the ice cube and thus more heat transfer. That is to say that water is a better conductor for heat to travel. Water can actually move 20 times faster than air, if all conditions are equal. An even better conductor for heat is glass or metal.