The Collaborative International Dictionary of English v.0.48:

Reindeer \Rein"deer`\ (r[=a]n"d[=e]r), n. [Icel. hreinn reindeer
   + E. deer. Icel. hreinn is of Lapp or Finnish origin; cf.
   Lappish reino pasturage.] [Formerly written also raindeer,
   and ranedeer.] (Zool.)
   Any ruminant of the genus Rangifer, of the Deer family,
   found in the colder parts of both the Eastern and Western
   hemispheres, and having long irregularly branched antlers,
   with the brow tines palmate.
   [1913 Webster]

   Note: The common European species (Rangifer tarandus) is
         domesticated in Lapland. The woodland reindeer or
         caribou (Rangifer caribou) is found in Canada and
         Maine (see Caribou.) The Barren Ground reindeer or
         caribou (Rangifer Groenlandicus), of smaller size, is
         found on the shores of the Arctic Ocean, in both
         hemispheries.
         [1913 Webster]

   Reindeer moss (Bot.), a gray branching lichen (Cladonia
      rangiferina) which forms extensive patches on the ground
      in arctic and even in north temperature regions. It is the
      principal food of the Lapland reindeer in winter.

   Reindeer period (Geol.), a name sometimes given to a part
      of the Paleolithic era when the reindeer was common over
      Central Europe.
      [1913 Webster]

WordNet (r) 3.0 (2006):

reindeer
    n 1: Arctic deer with large antlers in both sexes; called
         `reindeer' in Eurasia and `caribou' in North America [syn:
         caribou, reindeer, Greenland caribou, Rangifer
         tarandus]

Moby Thesaurus II by Grady Ward, 1.0:

49 Moby Thesaurus words for "reindeer":
   Cape elk, Siberian husky, Virginia deer, antelope, ass,
   beast of burden, buck, camel, camelopard, caribou, deer, deerlet,
   doe, draft animal, dromedary, eland, elephant, elk, fallow deer,
   fawn, gazelle, giraffe, gnu, hart, hartebeest, hind, horse, husky,
   kaama, llama, malamute, moose, mule, mule deer, musk deer, okapi,
   ox, pack horse, red deer, roe, roe deer, roebuck, sledge dog,
   springbok, stag, sumpter, sumpter horse, sumpter mule,
   wildebeest