Definitions of woolly:

• adjective:   covered with dense cottony hairs or hairlike filaments

  Example: "The woolly aphid has a lanate coat resembling cotton"

• adjective:   covered with dense often matted or curly hairs

  Example: "Woolly lambs"

• adjective:   having a fluffy character or appearance
• adjective:   confused and vague; used especially of thinking

  Example: "Woolly thinking"