'Cotton-eyed' as a descriptive adjective for having the whites of the eyes prominent was first noted in print in "Dialect Notes," 1905; older references are anecdotal.
Gargoyle noted this way back in 19 and 99 in this thread, and correctly identified the subject of the song as seduction.

Dorothy Scarborough, in "On the Trail of Negro Folk Songs" (1925) received anecdotal evidence that the song was sung by slaves on plantations in Texas and Louisiana. Since these sources were multiple, chances are good that it actually is an African-American party song from the 19th c.
In threads above is the excellent version collected by Scarborough as well as one from Talley, "Negro Folk Rhymes." N. I. White collected fragments from Blacks in Alabama in 1915-1916.

The song has not been found in minstrel routines as far as I can determine.

The party song has persisted among whites as a fiddle tune (multiple recordings in the 1920's), but with lyrics that no longer tell a complete story.