If the Water and Air are the same temperature, an ice cube will melt faster in the water. The molecules in a liquid are more densely packed than the molecules in a gas, which means that the ice cube makes more contact with molecules in water than in air.
Consider this variable: if the air is a higher temperature than the water, the ice cube would melt faster in the air.
If the air or water were below 32 degrees farenheit, the temperature at which water freezes, the ice cube would not melt at all!
Here is an experiment: An ice cube floaing in a glass of water touches both the air on top and the water below. As the ice cube melts, it sinks into the water, but if you keep it from sinking you will notice that the bottom part in the water is smaller, having melted faster, than the top part in the air.
Check out this EDUCATION.COM link to the fascinating Ice and Snow Study Guide.