I am not sure this is the origin, but...
In Tudor times, sleeves were not integral parts of women's dresses, but were tied on (easier to wash the sleeves alone, maybe) women could also change the look of an outfit by changing the sleeves. Perhaps the woman nicknamed "Lady Greensleeves" liked to where green sleeves with many of her dresses. Since it was fashionable to pay court to other men's wives, using a nickname could protect the not-so-innocent. Also, in terms of Henry VIII's wives and coverup sleeves, Anne Boleyn was reputed to have an extra finger.