I saw this question posted last week and I tried to find an answer for you (if same poster), but could not find anything conclusive. Fuzzy Wuzzy was a racist term for the natives of East Africa which invoked the shape/style of their hair. I could not find anything on the rhyme itself, though.

I have found that the term fuzzy wuzzy originated as slang from British troops for the Hadendoa.

Their elaborate hairdressing gained them the name of "Fuzzy-wuzzies" among the British troops during the Mahdist War. Osman Digna was a Mahdist general who led the Hadendoa to break a British infantry square in the Battle of Tamai, although he ultimately lost the battle itself. This was the inspiration for Rudyard Kipling's poem, Fuzzy-Wuzzy. They earned an unenviable reputation during the wars by their hideous mutilations of the dead on the battlefields.

Via Wikipedia

and I have found suggestions that the rhyme originated as a way to describe how the Hadendoa were so troublesome to the British troops.

The 'Fuzzy Wuzzy Falacy' is another name for Lanchester's Law, (Source in the disambiguation page of Fuzzy Wuzzy) which the below quote links to the poem. The following is not cited properly, merely found in the talk section of the Wikipedia article. It is however, the best explanation i have found so far.

I've heard the so called "Lanchester's Law" - the strength of a military force is proportional to the square of its numbers - cited as the "Fuzzy Wuzzy formula" long before the Gamasutra article cited in the "Lanchester's Law" article. As explained to me - by operations researchers working for the U.S. Department of Defense - the connection to the rhyme is as follows:

"Fuzzy wuzzy was a bear" - the fuzzy wuzzies gave the better trained British troops unexpected trouble.

"Fuzzy wuzzy had no hair" - the formula explaining why the fuzzy wuzzies did so well was a clean, square root relationship, not a complex, "hairy" one. The strength of the forces scaled only linearly with the firepower of the British troops, but with the square of the numerically superior fuzzy wuzzy troops.

"Fuzzy wuzzy wasn't fuzzy was he?" - play on words that the problem turned out not to be "hairy" after all.

This may have nothing to do with the origins of the nursery rhyme. Then again, lots of innocent British nursery rhymes in fact have origins in violent or gruesome incidents in British history - e.g., "Mary, mary quite contrary" and Mary Queen of Scots' refusal to cooperate after being imprisoned by her cousin Elizabeth I, resulting ultimately in Elizabeth's having Mary beheaded.

Warren Dew 04:50, 13 August 2007 (UTC)

I could not find another source for any of this however, not one with further citations.

You've got me interested now, so expect an update if I find more.

Edit 1; Found a source for 'Fuzzy Wuzzy Fallacy'. The term originated in a wargaming magazine called The Avalon Hill General in 1976, and while i found references to an earlier article apparently written about it, the mathematical formula they are using in this article are identical to the ones used in Lanchester's law. Page 13 of this issue is where the article starts. http://www.vftt.co.uk/Games/Avalon%20Hill/00%20The%20General/The%20General%20Vol%2013%20No%203.pdf