Seems like you guys need some evidence ...
Moist air is lighter than dry air - every pilot knows that, and that's why we have clouds up there in the sky.
BUT ... (isn't there always a 'but' ?) - the missing piece of the jigsaw which is so often overlooked is that of the evaporative cooling which occurs as moist air is formed. This cooling makes the molecules of water vapour denser, and thus heavier than air. Such air will then fall to the ground, or to the bottom of a box.
Here's an example where you can see such water vapour hugging the ground:
It will stay like that until 'the sun burns it off' - that is, until solar radiation reverses the heat loss, thus making that suspended moisture lighter than air again (and invisible), so that it rises high into the sky, where it cools at altitude and once again becomes visible as a cloud formation.
But in a box, there is no solar radiation, and so unless heat from the colony is sufficient to offset that cooling from evaporation (somewhat unlikely in winter), the moist air will remain at the bottom of the box - that is, unless some provision has been made for it to escape, of course.
Such cold moist air in winter causes black mould to form - always at the bottom of those boxes with solid floors:
And - if you want even more evidence of this phenomenon - check out the multi-billion dollar timber (lumber) seasoning industry which has it's origins in Oregon - where timber is treated with steam inside huge insulated sheds - with the excess moisture being drained-off ... again, always from the bottom.
Yes - you can allow moisture to escape from holes in the top of the hive, but this will be done at the expense of loss of heat. Which is an excellent idea during a summer in the tropics, but not so clever in more temperate regions. There are sound reasons why bees try their hardest to seal-up the tops of their hives with propolis. You can work with the bees, or against them - it's your choice, always.
LJ