The Collaborative International Dictionary of English v.0.48:

Air \Air\ ([^a]r), v. t. [imp. & p. p. Aired ([^a]rd); p. pr.
   & vb. n. Airing.] [See Air, n., and cf. A["e]rate.]
   1. To expose to the air for the purpose of cooling,
      refreshing, or purifying; to ventilate; as, to air a room.
      [1913 Webster]

            It were good wisdom . . . that the jail were aired.
                                                  --Bacon.
      [1913 Webster]

            Were you but riding forth to air yourself. --Shak.
      [1913 Webster]

   2. To expose for the sake of public notice; to display
      ostentatiously; as, to air one's opinion.
      [1913 Webster]

            Airing a snowy hand and signet gem.   --Tennyson.
      [1913 Webster]

   3. To expose to heat, for the purpose of expelling dampness,
      or of warming; as, to air linen; to air liquors.
      [1913 Webster]

The Collaborative International Dictionary of English v.0.48:

Airing \Air"ing\ ([^a]r"[i^]ng), n.
   1. A walk or a ride in the open air; a short excursion for
      health's sake.
      [1913 Webster]

   2. An exposure to air, or to a fire, for warming, drying,
      etc.; as, the airing of linen, or of a room.
      [1913 Webster]

WordNet (r) 3.0 (2006):

airing
    n 1: the opening of a subject to widespread discussion and
         debate [syn: dissemination, airing, public exposure,
         spreading]
    2: a short excursion (a walk or ride) in the open air; "he took
       the dogs for an airing"
    3: the act of supplying fresh air and getting rid of foul air
       [syn: ventilation, airing]

Moby Thesaurus II by Grady Ward, 1.0:

93 Moby Thesaurus words for "airing":
   Sunday drive, aerage, aeration, air conditioning, air cooling,
   amble, analysis, bandying, book, broadcast, broadcasting, bruiting,
   bruiting about, buzz session, canvassing, circulation, colloquium,
   conference, consideration, constitutional, cross-ventilation,
   debate, debating, deliberation, dialectic, dialogue, diffusion,
   discussion, display, dissemination, drive, evulgation, examination,
   exchange of views, forced march, forum, hike, investigation,
   issuance, issue, jaunt, joint discussion, joyride, lift,
   logical analysis, logical discussion, march, mush, open discussion,
   open forum, oxygenation, oxygenization, panel discussion, parade,
   perflation, periodical, peripatetic journey, peripateticism,
   pickup, printing, promenade, promulgation, propagation,
   publication, publishing, ramble, rap, rap session, refreshment,
   review, ride, saunter, schlep, seminar, spin, spread, spreading,
   spreading abroad, stretch, stroll, study, symposium, telecasting,
   town meeting, traipse, tramp, treatment, trudge, turn, ventilation,
   walk, walking tour, whirl