The Collaborative International Dictionary of English v.0.48:

Hairy \Hair"y\ (-[y^]), a.
   1. Bearing or covered with hair; made of or resembling hair;
      rough with hair; hirsute.
      [1913 Webster]

            His mantle hairy, and his bonnet sedge. --Milton.
      [1913 Webster]

   2. Very complicated, difficult, or involved; as, a hairy
      problem; a hairy equation. [Colloq.]
      [PJC]

   3. Dangerous or frightening; as, a hairy encounter with a
      mugger.
      [PJC]

WordNet (r) 3.0 (2006):

hairy
    adj 1: having or covered with hair; "Jacob was a hairy man"; "a
           hairy caterpillar" [syn: hairy, haired, hirsute]
           [ant: hairless]
    2: hazardous and frightening; "hairy moments in the mountains"

The Free On-line Dictionary of Computing (19 January 2023):

hairy

   1. Annoyingly complicated.  "DWIM is incredibly hairy."

   2. Incomprehensible.  "DWIM is incredibly hairy."

   3. Of people, high-powered, authoritative, rare, expert,
   and/or incomprehensible.  Hard to explain except in context:
   "He knows this hairy lawyer who says there's nothing to worry
   about."  See also hirsute.

   The adjective "long-haired" is well-attested to have been in
   slang use among scientists and engineers during the early
   1950s; it was equivalent to modern "hairy" and was very likely
   ancestral to the hackish use.  In fact the noun "long-hair"
   was at the time used to describe a hairy person.  Both senses
   probably passed out of use when long hair was adopted as a
   signature trait by the 1960s counterculture, leaving hackish
   "hairy" as a sort of stunted mutant relic.

   4.  hairy ball.

   [Jargon File]

   (2001-03-29)


The Jargon File (version 4.4.7, 29 Dec 2003):

hairy
 adj.

    1. Annoyingly complicated. “DWIM is incredibly hairy.”

    2. Incomprehensible. “DWIM is incredibly hairy.”

    3. Of people, high-powered, authoritative, rare, expert, and/or
    incomprehensible. Hard to explain except in context: “He knows this hairy
    lawyer who says there's nothing to worry about.” See also hirsute.

    There is a theorem in simplicial homology theory which states that any
    continuous tangent field on a 2-sphere is null at least in a point.
    Mathematically literate hackers tend to associate the term ‘hairy’ with the
    informal version of this theorem; “You can't comb a hairy ball smooth.”
    (Previous versions of this entry associating the above informal statement
    with the Brouwer fixed-point theorem were incorrect.)

    The adjective ‘long-haired’ is well-attested to have been in slang use
    among scientists and engineers during the early 1950s; it was equivalent to
    modern hairy senses 1 and 2, and was very likely ancestral to the hackish
    use. In fact the noun ‘long-hair’ was at the time used to describe a person
    satisfying sense 3. Both senses probably passed out of use when long hair
    was adopted as a signature trait by the 1960s counterculture, leaving
    hackish hairy as a sort of stunted mutant relic.

    In British mainstream use, “hairy” means “dangerous”, and consequently, in
    British programming terms, “hairy” may be used to denote complicated and/or
    incomprehensible code, but only if that complexity or incomprehesiveness is
    also considered dangerous.