The Collaborative International Dictionary of English v.0.48:

Hinniate \Hin"ni*ate\, Hinny \Hin"ny\v. i. [L. hinnire.]
   To neigh; to whinny. [Obs.]
   [1913 Webster]

The Collaborative International Dictionary of English v.0.48:

Hinny \Hin"ny\, n.; pl. Hinnies. [L. hinnus, cf. Gr. ?.]
   A hybrid between a stallion and an ass; -- correlative of the
   mule.
   [1913 Webster]

The Collaborative International Dictionary of English v.0.48:

Hinny \Hin"ny\, n.
   A term of endearment; darling; -- corrupted from honey.
   [Prov. Eng.] --Wright.
   [1913 Webster]

WordNet (r) 3.0 (2006):

hinny
    n 1: hybrid offspring of a male horse and a female donkey or
         ass; usually sterile; "a hinny has a gentler disposition
         than a mule"