The answer you seek is not so easily determined. There could be vapor transfer through the envelope of the room, due to differential vapor pressure and perhaps infiltration as well. Considering that you're posing this question after construction, it's possible (probable) that this envelope includes no vapor barrier - thus this load could be significant. Are doors and other openings equipped with seals? How often and for how long are the doors open? Are the barrels constructed of wood? What is their initial mass and moisture content? How often are the barrels exchanged? How many barrels? How much moisture is removed and not replaced by the cooling system? An invitation for sampling may yield better answers. It's not that far from here!