The Collaborative International Dictionary of English v.0.48:

Horse-radish \Horse"-rad`ish\, n. (Bot.)
   A plant of the genus Nasturtium (Nasturtium Armoracia),
   allied to scurvy grass, having a root of a pungent taste,
   much used, when grated, as a condiment and in medicine.
   --Gray.
   [1913 Webster]

   Horse-radish tree. (Bot.) See Moringa.
      [1913 Webster]

WordNet (r) 3.0 (2006):

horseradish
    n 1: the root of the horseradish plant; it is grated or ground
         and used for seasoning [syn: horseradish, horseradish
         root]
    2: coarse Eurasian plant cultivated for its thick white pungent
       root [syn: horseradish, horse radish, red cole,
       Armoracia rusticana]
    3: grated horseradish root