Should my mirror fog up when showering with a proper exhaust fan running?
Depends on:


The location of the fan relative to the shower and the mirror
The effectiveness of the fan
The air temperature in the room
The initial relative humidity of the room
The temperature and volume of the shower steam
The length of the shower
HVAC conditions
Window configuration (sunlight and airflow)


The bottom line is that it might, but it doesn't much matter as long as the fan is run long enough to reduce humidity after each shower. In my case (Minnesota), this means an hour in the winter and at least two in the summer (though maybe less when air-conditioning is active). A digital timer switch is very helpful.