He was a member of the Udall political family and was also a nephew of Spencer W. Kimball, the 12th President of the Church of Jesus Christ of Latter-day Saints.

His parents John Hunt Udall and Ruth Kimball were in the same English literature class at the St. Joseph Stake Academy (now Eastern Arizona College), and when learning about playwright Nicholas Udall, they joked that if they ever got married, that they would name their son Nick, which they did.

After graduation, he returned home to Arizona, where he began his law practice.

A lifelong member of the Church of Jesus Christ of Latter-day Saints, Nick served in various church positions, including service as a full-time missionary in the Eastern Central States mission from 1934 to 1936, as Bishop of the Phoenix Third Ward from 1970 to 1975 ("the most satisfying calling that a worthy priesthood holder can have" because "he is continually helping people"), and as Patriarch of the Phoenix Arizona Stake from 1975 to 1991.

Nick and his wife, Sybil Elizabeth Webb, are the parents of seven children.