The complete text of the carol can be found here. It seems that of the five verses, only verse one and three are included in the (english) Hymnbook (linked by OP).
This specific verse seems of rather trinitarian thought, that may be a reason. Seeing that two other verses have also been omitted:
Come, Desire of nations, come,
Fix in us Thy humble home;
Rise, the woman’s conqu’ring Seed,
Bruise in us the serpent’s head.
Now display Thy saving pow’r,
Ruined nature now restore;
Now in mystic union join
Thine to ours, and ours to Thine.
Adam’s likeness, Lord, efface,
Stamp Thine image in its place:
Second Adam from above,
Reinstate us in Thy love.
Let us Thee, though lost, regain,
Thee, the Life, the inner man:
Oh, to all Thyself impart,
Formed in each believing heart.
I don't know where to look for an authoritative answer, but the people responsible for Hymn books probably just didn't feel comfortable with the omitted verses. "Mystic union" is not in the vocabulary of mormons, and "Veil'd in flesh, the Godhead see" sounds too trinitarian, although it could be reinterpreted with a little effort. It's not so much that we couldn't sing these verses and reinterpret them with our doctrine, but it would not very comfortably.