Anyone trying to describe the smell would have to flounder among words like moisture, heat, vapour and, with a following wind, exhalation.
When air cools, its ability to hold moisture vapor decreases.
The paint will not help, because it is a vapor barrier: it keeps moisture vapor from passing through the wall from inside, but does not prevent condensation inside.
Wood is affected by liquid water in the form of rain, rivers, seas and so on with which it may come into contact but, more importantly, it is affected by the moisture vapour which is always present in the air.
Breathability is the ability of a fabric to allow moisture vapor to be transmitted through the material.
For example, if a bottle of vitamins contained any moisture vapor and was cooled rapidly, the condensing moisture would ruin the pills.
On the outside, latex paints are more resistant to peeling because they allow trapped moisture vapor to pass through the paint without blistering; oil paints are not permeable, so moisture trapped behind the paint may cause peeling.
Apart from moisture vapour, the air also contains millions of tiny plant spores which float around looking for somewhere to live and multiply.
The heating is a bonus, resulting from the release of latent heat as the moisture vapour condenses to liquid water within the machine, but dehumidifiers are not really heating devices - they are more effective in warm homes with high humidity levels than they are in buildings where low temperatures are the main problem.