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Personally I’d put one in because a window lets in loads of shitty cold air cooling everything around it and this helps moisture to condense on surfaces rather than drift away.
Whilst opening a window can let the steam out, depending on the wind direction, it can just as easily push the steam through the bathroom door into the rest of the house.
A fan is highly likely to always overcome any air pressure differential and extract the steam outside whatever the weather.
Do you have to have an extractor fan in a bathroom with a website? Bathroom has no issue with damp at the moment. Builder says we need one in there but it's quite pricey when you factor in the electrics.