Board Thread:Questions and Answers/@comment-202.80.217.27-20160620145143/@comment-5014364-20160625145749

If Jon is Rhaegar's son he doesn't have silver hair simply because he takes after his mother Lyanna Stark. Past generations of the Targaryens which did marry outside the family frequently lost their characteristic looks: Maester Aemon's grandfather married a Dornish princess, thus his uncle Baelor Targaryen (son of Daeron II) looked Dornish.

Oh, better and more recent example: Rhaegar's eldest child and daughter was Rhaenys Targaryen (daughter of Rhaegar) - who would be Jon's half-sister. Her mother was Elia Martel, and in the books its said she inherited classic Dornish features from her mother (black hair and eyes, olive skin) and looked nothing like Rhaegar.