I agree with Jim that a timer or a hygrometer-triggered shutoff is the only way to go, in the long term. Nobody wants to have to "go to the bathroom" twice, the second time just to handle the air system. By this, I mean turn it off.
Molo, in terms of your priorities, i think you will want to focus on how your building handles air in broadest sense of the term "handle". Every time you create a new opening to the outdoors you are allowing convection (warmer air rises) to push your indoor air to the outside, all the time, even when the fan is off. Replacement air comes from somewhere else in the house, although rarely you can have a slow return current in the vent conduit itself. Inside a (3", 4", or larger, bathroom kitchen or dryer) vent there is usually a single direction of flow; it may seem very slow to you on a "normal" day but it is always ON by the fact that it is always OPEN, and it loses a lot of air to the outside. Furthermore, the air flow can be extremely fast and powerful without any motors pushing air. Pressure differentials are normal in nature, and that's what makes wind blow, and that's what sucks air out of your house on one side and pushes it in somewhere else.
The other big air openings in the house are probably in the kitchen (over the cooktop), and for the fireplace / wood stove / heating system. In my place, sometimes (rarely) air comes down one of these vents when it is needed to fill the void created by another vent... so it really is a good idea to plan for a heat exchanger / air exchanger system, as they equalize pressure automatically. It is pretty ugly when a fireplace not in use lets air come down the chimney spreading the odor of soot and ashes throughout the house -- this happens every year, in my house. Yes, there is a damper that closes the flue, and even if I seal the fireplace off with tape, there is still a lot of air pressure pushing air inside... Could be because of how wind blows around the vents above, or the fact that the chimney area is the coldest corner and that lets convection push air up out of the other vents first, causing a negative pressure.... The point to remember is that you might want to be able to close the vent entirely at certain times, and that whole-house air/heat exchangers are good to have in very cold climates.
Don't worry too much about eliminating moisture. yes, it is important to exchange air in the bathroom, to get rid of the moisture, but no, it is not the single most important thing to focus on, in a cold climate where you need to conserve heat and plan for makeup air to come in when a fan is pushing air out. Handling air exchanges, air flow, airtightness, and insulation, is just as important.
Water vapor is invisible at most concentrations, and it is the lightest gas in the air so it rises fast. To repeat this: O2, N2, CO2 are all heavier than H20 in gaseous form. This explains why wator (vapor, humidity, moisture, condensation, etc) is a problem upstairs or in attics when a house has too much humidity. You cannot get rid of humidity, since you breathe all the time and this puts moist air into your house. I bought a home hygrometer and it taught me a lot. One thing being not to worry about the general humidity level in the winter.
Is your building leaky or airtight? Modern or old? Do you have a whole house air handling system, or do you rely on air leaking and doors opening to exchange air? How well insulated is the house?
david