The Collaborative International Dictionary of English v.0.48:

Woolly \Wool"ly\, a.
   1. Consisting of wool; as, a woolly covering; a woolly
      fleece.
      [1913 Webster]

   2. Resembling wool; of the nature of wool. "My fleece of
      woolly hair." --Shak.
      [1913 Webster]

   3. Clothed with wool. "Woolly breeders." --Shak.
      [1913 Webster]

   4. (Bot.) Clothed with a fine, curly pubescence resembling
      wool.
      [1913 Webster]

   Woolly bear (Zool.), the hairy larva of several species of
      bombycid moths. The most common species in the United
      States are the salt-marsh caterpillar (see under Salt),
      the black and red woolly bear, or larva of the Isabella
      moth (see Illust., under Isabella Moth), and the yellow
      woolly bear, or larva of the American ermine moth
      (Spilosoma Virginica).

   Woolly butt (Bot.), an Australian tree (Eucalyptus
      longifolia), so named because of its fibrous bark.

   Woolly louse (Zool.), a plant louse (Schizoneura lanigera
      syn Erisoma lanigera) which is often very injurious to
      the apple tree. It is covered with a dense coat of white
      filaments somewhat resembling fine wool or cotton. In
      exists in two forms, one of which infests the roots, the
      other the branches. See Illust. under Blight.

   Woolly macaco (Zool.), the mongoose lemur.

   Woolly maki (Zool.), a long-tailed lemur (Indris laniger)
      native of Madagascar, having fur somewhat like wool; --
      called also avahi, and woolly lemur.

   Woolly monkey (Zool.), any South American monkey of the
      genus Lagothrix, as the caparro.

   Woolly rhinoceros (Paleon.), an extinct rhinoceros
      (Rhinoceros tichorhinus) which inhabited the arctic
      regions, and was covered with a dense coat of woolly hair.
      It has been found frozen in the ice of Siberia, with the
      flesh and hair well preserved.
      [1913 Webster]

WordNet (r) 3.0 (2006):

woolly
    adj 1: having a fluffy character or appearance [syn:
           flocculent, woolly, wooly]
    2: confused and vague; used especially of thinking;
       "muddleheaded ideas"; "your addled little brain"; "woolly
       thinking"; "woolly-headed ideas" [syn: addled, befuddled,
       muddled, muzzy, woolly, wooly, woolly-headed,
       wooly-minded]
    3: covered with dense often matted or curly hairs; "woolly
       lambs" [syn: wooly, woolly, wooly-haired, woolly-
       haired]
    4: covered with dense cottony hairs or hairlike filaments; "the
       woolly aphid has a lanate coat resembling cotton" [syn:
       lanate, woolly]

Moby Thesaurus II by Grady Ward, 1.0:

22 Moby Thesaurus words for "woolly":
   bristly, bushy, cirrose, downy, feathery, fleecy, flocculent,
   flossy, fluffy, furry, fuzzy, hairy, hirsute, hispid, lanate,
   matted, pilose, pubescent, shagged, shaggy, unshorn, whiskered