Moses - 1

 As I have noted previously, the Lord revealed that an angel or heavenly messenger - 

"...be the spirit of a just man made perfect he will come in his glory; for that is the only way he can appear—"  (Doctrine and Covenants 129:6)

Apparently, a spirit can only reveal himself in his glory.

We learn that as Moses was caught up to an exceeding high mountain - 

"...he saw God face to face, and he talked with him, and the glory of God was upon Moses; therefore Moses could endure his presence."  (Moses 1:2)

Obviously, the Savior or Jehovah was still a spirit only.  Thus, He would appear in His glory.  For this to take place, the requirement then would be for Moses to be "transfigured" to endure His presence.

Elder Bruce R. McConkie taught - 

“Transfiguration is a special change in appearance and nature which is wrought upon a person or thing by the power of God. This divine transformation is from a lower to a higher state; it results in a more exalted, impressive, and glorious condition.… “By the power of the Holy Ghost many prophets have been transfigured so as to stand in the presence of God and view the visions of eternity” (Mormon Doctrine, page 803).

This explains why Peter, James, and John were able to witness the heavenly visits on the Mount.