I have been thinking about this, and how to put it to him so that he accepts that it is a scientific answer and not just a mere wife repeating old wives tales.
When hot water is run it produces water vapour, which rises to mingle with the dryer air already in the room. Air can only hold so much water vapour before it get over-saturated - and cold air can hold less than warm air - scientific fact. When the warm wet air comes in contact with a cold surface, it drops some of the water vapour as drops of water (probably with a sigh of relief as it does so.)
Very hot water run into a shallow container, like a bath, lands with a splash, sending lots of steam and water vapour up into the air. That hot water spreads out over the base of the bath, with plenty of surface area to mingle more water vapour with the air. It rises (because it is warm and warm air rises -* scientific fact*) and reaches the window. It can't rise right up and out because the window is closed, but the glass is nice and cold, so it condenses out and runs down in streams. If the window had been open most of it would have gone up and out
If you run cold water first (even a shallow layer of one inch or so) the very hot water falls into cold water, not onto a shiny bath surface so it 1) doesn't splash up so much and mix water vapour so readily with the dry air and 2) is cooled a little by mixing into the cold water, so it doesn't produce as much water vapour
And if you both open a window while you fill the bath and add a layer of cold before the hot, you achieve both of these improvements (and you wife stops nagging you about the waterfalls in the bathroom)
If you also open a window after your bath, too, the warm damp air remaining in the bathroom has a way to escape out of the window before the air cools down so far that it is no longer able to support any water vapour at all and drops it as condensation onto the cooling walls, floor, basin, toilet seat, doorhandle, loo roll . . . . .