Help...have read in the past the exhaust fans in bathrooms generally aren't that effective. In other words, by simply ensuring the door is left open after a shower, as much humidity can be removed from the room as an exhaust fan could.
I live in Northeastern Wisconsin. Opening a window is not a year round solution. Am concerned with the efficiency (or lack of) an exhaust fan during the winter months. I also have a teenaged daughter that believes it's necessary to blow dry her hair for 20 minutes after her shower. So not only is the room a bit on the humid side, it gets heated by the dryer.
I know in Maryland that they were required by code, and further they were required to the come on when you switched the main lights on. To make an intelligent comment one would really have to take a look at your house to see how well the humidity "drains" w/o a fan or window left open. One thing to keep in mind is that during the winter the glass in your windows will be cold enough for that humidty to immediately condense and run down onto the stool and probably into the window itself. That's never going to be a good thing.
You have to balance the cost of losing the heated air against those of possibly having to repaint more often, possibly having your window rot, possibly having moisture migration into the drywall, etc. etc. etc.
It may be that the way your house's natural ventilation is that you are just fine not using a fan. On the other hand it may be that your bathroom turns into a steam room. Tough to tell from here.
While the idea of opening the door while showering may be effective (and again I don't know the layout of your house) the first time a guest happens to spy your daughter stepping out of the shower may put an end to that strategy.
The heat of your daughter's hair dryer isn't going to change the siutation any. All heat does is convert water to gas so it can escape more easily. If there is nowhere for the gas to escape to, i.e. insufficient ventilation, it's going to recondense in that room as soon as the temperature goes back down 20 minutes later.
Lots of variables here but they don't insist on bathroom ceiling fans in the code for no reason.
good luck

ml