Notso, quite agree with you that the 'down flow' and subsequent further cooling of the air causes the condensation to build from the bottom of the glass.
Genghis did also state this reason in the second part of his post. I agree with you that it is a secondary and most likely barely perceptible cause.
As I said the theory is sound, but I feel too tiny to be influential in practice.
To further confirm CJ Driver on his reasoning behind the air conditioning question, have you ever been stationary in your car with the air con running then reversed? If so you may have noticed a considerable damp spot on the ground where the front 1/3 of the car was. This is indeed where the intake air is passed over the cooling element and in doing so is stripped of its moisture as it hits dew point, the moisture condenses onto, then drips from the element into a collector tray and is discharged though a drain pipe to waste (the ground) under the vehicle. Result; dehumidified air with a large moisture carrying capacity passing over the screen stripping away any moisture present there.
When you turn the a/c off the opposite tends to happen for a short while, the air begins to strip the moisture from the element and deposit it on the windscreen as the air is now carrying ambient moisture plus an additional load making it keen to give this excess moisture load up, very annoying that little quirk I find. Freeze or fog the screen for a few minutes.
Correction to answer the question as actually asked:
The difference between the warm and cold 'conditioned' air is most likely that the warm air is added in after the cooling process, therefore putting moisture carrying air back into the mix so although the air is warm it carries more moisture than the 'pure' conditioned and dehumidified air. There will obviously be a transitional phase and change over point where the heat of the 'wet warm' air will have a superior 'drying' effect than the 'stripping' effect of the 'cold but dry' air.