The Collaborative International Dictionary of English v.0.48:

Owling \Owl"ing\, n. [From Owl, v. i.] (O. Eng. Law)
   The offense of transporting wool or sheep out of England
   contrary to the statute formerly existing. --Blackstone.
   [1913 Webster]

The Collaborative International Dictionary of English v.0.48:

Owl \Owl\, v. i. [imp. & p. p. Owled; p. pr. & vb. n.
   Owling.]
   1. To pry about; to prowl. [Prov. Eng.]
      [1913 Webster]

   2. To carry wool or sheep out of England. [Obs.]
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   Note: This was formerly illegal, and was done chiefly by
         night.
         [1913 Webster]

   3. Hence, to carry on any contraband trade. [Eng.]
      [1913 Webster]

Bouvier's Law Dictionary, Revised 6th Ed (1856):

OWLING, Eng. law. The offence of transporting wool or sheep out of the
kingdom.
     2. The name is said to owe its origin to the fact that this offence was
carried on in the night, when the owl was abroad.