Huntsman was never the nominee and never close to getting the nominee. He was never vetted for president because he was a waste of air.
Your question was “how many mormons have run before Romney”, it was not who had a chance to win or who was vetted.
George Romney
Harry Reid
Orin Hatch
Mitt Romney twice
Joseph Smith
Morris Udall
Ezra Taft Benson
Parley P. Christiansen
Eldridge Cleaver
Sonia Johnson
James G. Gritz