The Collaborative International Dictionary of English v.0.48:

Woo \Woo\, v. t. [imp. & p. p. Wooed; p. pr. & vb. n.
   Wooing.] [OE. wowen, wo?en, AS. w?gian, fr. w?h bent,
   crooked, bad; akin to OS. w[=a]h evil, Goth. unwahs
   blameless, Skr. va?c to waver, and perhaps to E. vaccilate.]
   [1913 Webster]
   1. To solicit in love; to court.
      [1913 Webster]

            Each, like the Grecian artist, wooes
            The image he himself has wrought.     --Prior.
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   2. To court solicitously; to invite with importunity.
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            Thee, chantress, oft the woods among
            I woo, to hear thy even song.         --Milton.
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            I woo the wind
            That still delays his coming.         --Bryant.
      [1913 Webster]

WordNet (r) 3.0 (2006):

wooing
    n 1: a man's courting of a woman; seeking the affections of a
         woman (usually with the hope of marriage); "its was a brief
         and intense courtship" [syn: courtship, wooing,
         courting, suit]