With it being that cold are you sure that the humidity is 53%
This seems alfully high espically if the heat in your home is on
Do you have a humidifier also ?
Do you have any other vents in the attic ?
Such as ridge vents/soffit vents
secondly, if you do not have a dehumidifier get one and use it in the basement, these two things will stop moisture from migrating into the attic.
Other things to consider are to make sure everyone uses bathroom and kitchen ventilation fans (check to be sure they all terminate at the exterior) as a added measure add timers to all bath fans and let them run 20 min. after showering or bathing. These area's contribute to moisture build up in the attic. If you are sure there is adequate ventilation in the attic area's then you won't even need the attic fan.
If the vents are adequate then there shouldn't be any air moving from inside tour home
From what you have told me there is
I would check to make sure that there is adequate space for your fan's output