How does a Hidden Mist ninja have the Byakugan?
Yes, there is a mention of such a ninja in the manga as well as in the earlier episodes of the anime.

The ninja that you are referring to is Ao. 


  He has clashed several times with Konoha shinobi. At one point he
  defeated an unknown Hyūga, taking one of the Hyūga's Byakugan and
  implanting it into his own right eye socket. Later, he had a
  confrontation with Shisui Uchiha, which left enough of an impact on Ao
  for him to clearly remember Shisui's abilities and his chakra colour
  long after the event.


He first appeared in the manga chapter 454 and Naruto Shippuden anime episode 199 (the five kage summit arc)