I've got a 2010 Octavia S (i.e. bottom of the range, as few bells and whistles as possible!).

When the fan is on, temperature knob set to something warm (i.e. not to cold), when the right hand knob is turned to the windscreen position, the light on the air conditioner button usually (but not always) comes on. Don't know if the air coming out is cooled (what would win? the hot air via the engine or the air conditioning?) as I always deselect it.

The manual says nothing about using the air con to 'demist' or 'dehumidify' the air to demist the windscreen. The chap I spoke to at the Skoda dealers thought it could be some kind of dehumidifying function, but didn't know. I wondered if anyone on here knew anything about it, as it is a bit of a faff to take it to the dealers to get them to look at it (espeically if it IS operating as intended!).

The car has no climate control or anything fancy like that fitted.

It is an Air conditioner - that does not mean it has to be cold. When you point to the windscreen it will always come on as it will demist the screen a lot quicker with it on than off...

Even if you set it to hot with AC on, it will clear the screen quicker as it will dry the air, that does not mean it's pushing cold air.

As already mentioned, the system is working as designed. Aircon is not just for cooling in the summer, it removes moisture from the air in winter. The AC in my car is never turned off, and its always nice and mist free inside no matter how many passengers or how damp it is outside. However below 4c the aircon compressor is disabled, so below this temperature the AC will not help the screen demist at all since its disabled to stop ice forming inside the compressor.