I do recommend running the fan at night, as the breeze and fresh air will benefit the plants night and day. One thing to keep in mind is warmth, you don't want the fan cooling off the plants too much at night (a digital thermometer with high/low memory can help you).
As for the moisture comment...the fan would help moisture evaporate, but a fan in and of itself will not creature moisture to the best of my knowledge.
I run exhaust fan 24/7, circulation fan off at night.
I can do that because I don't have humidity issues, and the plants seem to like it.
The air in my tents is exchanged completely about twice per minute, so there's no lack of fresh air as long as the exhaust fan is running, but the circulation fan can be off.