Water droplets appearing outside a glass of ice water are caused by water-vapor molecules in the air.
When we put cold water in a glass, a temperature difference is established between the inside of the glass and its outside. Water molecules dispersed in the air, when they find a cooler surface, end up providing heat to it.
This causes them to condense - to the liquid state - and water droplets to appear on the outer walls of the glass. This phenomenon can also be observed when on a cold winter day we turn on a car's air conditioner: the glass also gets sweaty