Does an activated carbon filter in a kitchen hood dry the air?
All the moisture will head right back around if you are (as seems to be the case) talking about one of those useless hood-shaped objects that don't actually vent outside. Carbon does not trap water, and if it did, or you put in something that did, you'd have to change it very, very frequently. 

Indeed, the "filtration" provided by such hood-shaped objects is fairly ineffective, period. Burn something on the stove and the smoke will hang around for a long time.