The Collaborative International Dictionary of English v.0.48:

Grog \Grog\ (gr[o^]g), n. [So named from "Old Grog" a nickname
   given to Admiral Vernon, in allusion to his wearing a grogram
   cloak in foul weather. He is said to have been the first to
   dilute the rum of the sailors (about 1745).]
   A mixture of spirit and water not sweetened; hence, any
   intoxicating liquor.
   [1913 Webster]

   Grog blossom, a redness on the nose or face of persons who
      drink ardent spirits to excess. [Collog.]
      [1913 Webster]

WordNet (r) 3.0 (2006):

grog
    n 1: rum cut with water