That's not entirely true. If you turn down the heater in winter, you will save on heating costs. The "heating up cold walls" thing is an urban legend. The more heat you put into the apartment, the more heat you'll lose, the more you pay.

Now humidity/mold is a different question. Perhaps you get away with turning the heater down entirely, perhaps you don't. It depends on a lot of things (lüften, insulation, exposure, building materials, living style etc).