More can always be said, but this older answer might be of interest for you.

So if you're referring explicitly to the KKK robes, those were developed during the Second Klan in the years following the film The Birth of A Nation (1915). This film is widely considered one of the most racist of all times, and it depicts members of the First Klan, which unlike our popular conception of the Klan, was really just a loose association of white supremacists who formed decentralized groups with the intention of upholding the white supremacist system which dominated the South before Reconstruction. In fact, many of these groups did not even go by the title Ku Klux Klan. These folks didn't have the outfits which we associate with the KKK today. Those robes were actually a total fabrication for the film and it became, as my undergrad thesis advisor aptly put it, "the original cosplay." During the terror of the First Klan, many of these folks did not attempt to cover their faces and in many instances made no effort at all to conceal their identity to instill more terror in Black victims - these people knew they could operate with impunity and putting that in full force was a powerful effort. The Second Klan chose to coopt the hoods which we are familiar with because of the popularity of The Birth of a Nation, which popularized the hoods and gave them an easily-identifiable meaning without revealing the identity of the wearer (though it was generally pretty much common knowledge if you were in the Klan in many parts of the South during the Second Klan).

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For more on the First Klan, good primary source documentation would definitely be the KKK hearings. The federal government did an inquest in the role of white supremacist terror in the South during Reconstruction and made an effort to get victims to testify and get their testimony recorded for public record.