The joker never had red hair!!! Helmut yes!

The Red Hood first appeared in Detective Comics #168 "The Man Behind the Red Hood" (February 1951). In the original continuity, the man later known as the Joker was a master criminal going by the alias of the Red Hood. His costume consisted of a large domed red helmet and a red cape. While attempting to rob a chemical plant, his men were dispatched and then he was suddenly cornered on a catwalk by Batman. Left with no alternatives, he dove into a catch basin for the chemicals and swam to freedom, surviving because of a special breathing apparatus built into the helmet. The toxins in the vat permanently discolored him, turning his hair green, his skin white and his lips red. Upon discovering this, he went insane, and adopted the persona of the Joker.

[link to en.wikipedia.org]

Now as a joker fan you would know he was called the man in red hood and then later became the green haired joker.