Why do we describe a problem or experience as "hairy"?

Robert Hendrickson, The Facts on File Encyclopedia of Word and Phrase Origins (1997) offers this analysis:

hairy. Hairy, as slang for unpleasant or rough, seems to be of Army origin, from about 1935, when a hairy patrol was an unpleasant one that met with resistance. Its origin is unknown, but the word may have something to do with to make one's hair stand on end and "scary." Another possibility, a longshot, is the English expression hairy at the heel, common in the late 19th century. A horse with hair about the heels or fetlocks was an underbred one, so the expression was used figuratively for an ill-bred, bad-mannered, thoroughly unpleasant person, as was hairy.

Eric Partridge, A Dictionary of Slang and Unconventional English (1961) confirms that the meaning of "hairy about the fetlocks," is "ill-bred, bad-mannered," and says that it comes "from the stables"; but he distinguishes that meaning of hairy (which he traces to the late 1890s) from the earliest meaning—"difficult"—which he says comes from Oxford University, circa 1850–1900.

An earlier work by Partridge, Slang To-day and Yesterday (1933) puts the dates for hairy as "difficult" as 1840–1870), suggesting that it had fallen into disuse by the turn of twentieth century:

Hairy. Difficult : Oxford, 1840–1870. N., a draught horse: C[entury] 20.

John Farmer & William Henley, Slang and Its Analogues Past and Present (1893), also list "difficult" as the earliest slang meaning of hairy, and offer two early instances of that usage:

Hairy, adj. (Oxford University).—1. Difficult

[Example:] d. 1861. Arthur Clough, Long Vacation Pastoral. Three weeks hence we return to the shop and the wash-hand-stand-bason, Three weeks hence unbury Thicksides and HAIRY Aldrich.

[Example:] 1864. The Press, 12 Nov. HAIRY for difficult is a characteristic epithet.

Other nineteenth-century meanings of hairy reported in Farmer & Henley include "Splendid; famous; conspicuous; uncommon" and [of women] "Desirable; full of sex."

None of the early editions of John Camden Hotten's Slang Dictionary (published in London between 1859 and 1874) contains any entry for hairy—even though hairy in the sense of "difficult" appears to be a survival of English university slang from roughly that era.