Could the cup's water leak out?
From the conclusion, the water on the surface of the cup is derived from the air. In very dry desert, dew does not occur.
If you put the ice in the cup, the surface of the cup becomes cloudy after a while because the water vapor in the air condense and become droplets.
When the temperature decrease, the amount of water vapor that can be contained in the air is reduced. Then some water vapor condense and become water.
The temperature at which water vapor begins to condense is called the dew point.