And while we’re at it:
Where did he come from?
Where did he go?
Back when we all used to smoke pot, it was commonplace to call the dry-mouth affect “cottonmouth”, pretty much the same thing happens to your eyes and that’s why they turn red (they dry out). We started calling it “cotton-eye”. Maybe Joe was a stoner.
Call me crazy, but… (:: crowd: “You’re crazy!” :: 
) I think that children’s song has been around longer than the 1960s. Joe in that song is dead, so perhaps his eyes were rolled back in his sockets, or had rotted out and were replaced with spider webs. Hell, maybe he had really bad cataracts. 
Maybe, and this is what I think, the song is just semi-nonsensical and they used words that sounded good and filled time.
Most sources just say it is a traditional fiddle tune, dance song. All I could track down is that it was such by 1925.
But Lighter, RHDic AM Slang, says that it appears in Dialectic Notes III in 1905 as a Southern adjective meaning “Having the whites of the eyes prominent.”
Cottoneyed Joe is a dance…not a person.
Just so I my post wasn’t misunderstood, “cotton-eyed” was an expression 1n print by 1905.
It is in fact an old fiddle tune that was redone in the version that is pretty common today. I don’t really have anything else to add though.
Here’s another angle. I saw a TV concert by a female singer whose name escapes me. Before singing the song (yup, there are words,) she explained her take on its meaning. Cotton-eyed, she said, meant blind, probably by cataracts. Furthermore, she believed that a line in the song suggested Joe was an illegal abortionist. The line said something like, “If not for Cotton-Eyed Joe, I’d o’ been married.” The singer also surmised that Joe (or Jo) was a woman. Now, that might seem like a whole lot of surmising. However, I’m just presenting the singer’s opinion for your perusal.
Thanks for the replies, everyone. I have a little trouble believing that the reference is to anything but handsomeness, though, if these are the lyrics:
If it hadn’t been for Cotton-Eyed Joe
I’d a’ been married a long time ago
Where did you come from? Where did you go?
Where did you come from, Cotton-Eyed Joe?
(repeat)
He came to town like a midwinter storm
He rode through the fields so handsome and strong
His eyes was his tools and his smile was his gun
But all he had come for was having some fun
(repeat intro)
He brought disaster wherever he went
The hearts of the girls was to hell broken sent
They all ran away so nobody would know
And left only men cause of Cotton-Eyed Joe
(repeat intro)
Possibly related to the southern intransitive verb “cotton” (a liking) as in take a cotton to?
Women took a cotton to Joe 'cause of his pretty eyes.
Those folks do talk kinda funny, you know. 
Gotta cotton to them, though.
Peace,
mangeorge
Far away and long ago,
On the trail to the Alamo
Met a gal I used to know,
Ridin’ on a Cotton-eyed Joe
Chorus:
|: Cotton-Eyed Joe,
Cotton-Eyed Joe,
Gimme that gal,
Cotton-Eyed Joe.
–To further muddy the waters this “Texas” version suggests that Joe was a horse.
See, now, the lyrics I remember as a child went:
I always assumed the second verse was a response from Joe.
But then, we always sang the lyrics to a slow, mournful, guitar-strumming tune, not a high-steppin’ fiddlin’ tune. (A la the techno song that repopularized it in the last few years.)
That was Michelle Shocked. She’s a relatively feminist/activist semi-folk singer, so this may color her take on the etymology. The reasoning sounded pretty dubious to me.
Now the “Cottoney Joe” by Rednex(!) is playing in my head. The horror, the horror.
Thanks a lot ElvisL1ves I’m gonna get you for this…
Yes, that was Michelle. I saw her in concert shortly before Arkansas Traleler was released and she told the same story, except that the doctor/abortionist is blindfolded, (so he can claim to not know where he was) rather than actually blind. I don’t believe, though, that she presented this as the “true story” behind the lyrics, but merely her own take on a traditional song.
Her version, Prodigal Daughter (Cotton Eyed Joe) includes the traditional version as the chorus, with what I believe are her own lyrics added to flesh it out. Her rendition is obviously about abortion, with the prodigal daughter coming home “with the seeds he’s sown” and “bringing such shame to the family name.”
It’s a great album, by the way.
I grew up in semi-rural North Carolina. The rural/folk tradition of music is alive and well. Yes, some people still sit out on their front porch playing and singing traditional folk songs, if it’s a neighborly affair others may join them. Think “Andy Griffith” but no so hokey. (And no, I’ve never met the kid in Deliverance.)
In my experience, “Cotton Eyed Joe” was a recurring character in several songs and/or stories. This is fairly common in folk music/stories, where a specific character is freely used by different authors/writers/etc (used by anyone who wants to, really). Examples: “Flora” who is usually portrayed as an unfaithful girlfriend/wife, “the Blackjack Davie” or “the Gypsy Davie” who is a rake and a scoundrel but the lord of the manor’s wife runs off with him anyway, and “Jack” of “Jack and the Beanstalk”. There are actually quite a few “Jack” stories, and new ones are made up all the time. These characters appear in different stories or songs, although often with similar themes (e.g. the faithless Flora).
Cotton Eyed Joe is another such character, and his various exploits have been documented by others in this thread.
However, the OP asked “How’d he get cotton eyed?” Someone else suggested it was because he had pretty eyes and the women took a cotton to him.
IMHO, “Cotton Eyed” was just a descriptive nickname for Joe, nothing more. Kind of like “Bucktooth Charlie”, “Tricky Dick”, or “Large Marge”, it was just a nickname. He may have had eye trouble of some sort, but I don’t remember that being mentioned in any lyrics.
As evidence of how the folk process works, I found the following variations on the Cotton-eyed Joe theme on the net.
“If it hadn’t been for Cotton-eyed Joe,
I would have been married N years ago”
because…
Protagonist is a woman who was betrayed by Cotton-eyed Joe.
Protagonist is a guy whose girl ran off with Cotton-eyed Joe.
Protagonist is a woman whose father (probably) shot Cotton-eyed Joe.
Protagonist is a woman who got an abortion provided by Cotton-eyed Joe (Michelle Shocked version – nothing else even remotely similar found on the net).
Finally, no information at all on what it means to be “Cotton-eyed” except for one site that implied that Cotton-eyed Joe was a “hoodoo” man who charmed the ladies despite being crippled and/or blind by means of magic.
Here’s lyrics from the Mudcat Cafe:
This still doesn’t answer the OP but it’s another version of the song (hinting that Joe was a slave?)
Also I agree with the posters who suggested he had “cotton” in his eyes for the ladies.
What I get from these lyrics is what Finagle says. I agree
I tend to agree with Jimbrowski. Often the simplest answer is the right one, and southerners are keen on nicknames.
Cotton-eyed could mean no more than that the character had very pale blue eyes.
All these yankees, frettin’ over a song. Ain’t that a caution.
Peace,
mangeorge