The Collaborative International Dictionary of English v.0.48:

Dampness \Damp"ness\, n.
   Moderate humidity; moisture; fogginess; moistness.
   [1913 Webster]

WordNet (r) 3.0 (2006):

dampness
    n 1: a slight wetness [syn: damp, dampness, moistness]

Moby Thesaurus II by Grady Ward, 1.0:

23 Moby Thesaurus words for "dampness":
   bogginess, damp, dewiness, exudation, fogginess, humectation,
   humor, marshiness, mistiness, moistiness, moistness, moisture,
   rainfall, raininess, showeriness, soddenness, sogginess, soppiness,
   swampiness, wateriness, wet, wetness, wettishness