The Collaborative International Dictionary of English v.0.48:

Riding \Rid"ing\, a.
   1. Employed to travel; traveling; as, a riding clerk. "One
      riding apparitor." --Ayliffe.
      [1913 Webster]

   2. Used for riding on; as, a riding horse.
      [1913 Webster]

   3. Used for riding, or when riding; devoted to riding; as, a
      riding whip; a riding habit; a riding day.
      [1913 Webster]

   Riding clerk.
      (a) A clerk who traveled for a commercial house. [Obs.
          Eng.]
      (b) One of the "six clerks" formerly attached to the
          English Court of Chancery.

   Riding hood.
      (a) A hood formerly worn by women when riding.
      (b) A kind of cloak with a hood.

   Riding master, an instructor in horsemanship.

   Riding rhyme (Pros.), the meter of five accents, with
      couplet rhyme; -- probably so called from the mounted
      pilgrims described in the Canterbury Tales. --Dr. Guest.

   Riding school, a school or place where the art of riding is
      taught.
      [1913 Webster]

WordNet (r) 3.0 (2006):

riding school
    n 1: a school where horsemanship is taught and practiced