The majority of the steam, by design, is kept inside the cabin. The major escape of steam would be when exiting after a sauna session. If you simply wait a few minutes before exiting, the steam will vapourise on the cabin walls and dissipate.
A steam shower would be similar to a regular shower and with good ventilation, you should not experience any moulding or moisture damage, this is, however, different for all and dependant on the bathroom. Fixtures made from porous wood are of course more at risk.
Additional extractor fans would help in bathrooms where fixtures and ventilation are not ideal