Somebody correct me if I'm wrong here...
With the bathroom type fans that are designed to pull moist air outside, doesn't it also mean that cold air is being pulled into the house somewhere? It's not like the fan is only putting moisture outside, it's also putting heated air outside.
It might cost less in electricity to run a fan compared to a humidifier, but your furnace will probably run more often and make your gas bill correspondingly higher. I'd go with the dehumidifier, because it will reduce the humidity, but it will also heat the fish room and cut down the amount that your heaters will have to run.