Question

When saturated air is cooled what happens to its dew point

Answer 1

When saturated air is cooled, it simply reaches its dew point. Dew point is simply the temperature at which dew begins to form.

Dew point of saturated air is already pre-determined by how much water vapor the air contains. A  state of saturation exists when the air is holding the maximum amount of water vapor possible at the existing temperature and pressure. The higher the dew point, the higher the moisture content of the air. Cooling does not change the dew point of saturated air, rather its the level of saturation. 

So if the air has more moisture, dew will form at a higher temperature and vice versa, but dew point is NEVER EVER GREATER than the air temperature.