The early mormon church was rabidly anti-Christian and quotes by the leaders prove that. I think that recognition and use of the cross as a symbol would have been anathema to them.
The "official" explanation is: "Latter-day Saints do not use the symbol of the cross in their architecture or in their chapels. They, like the earliest Christians, are reluctant to display the cross because they view the "good news" of the gospel as Christ's resurrection more than his crucifixion."
Mormons have come up with a substitute for cross jewelry: A small committee of women came up with the idea of the CTR rings in 1970. CTR, or Choose the Right, is the name of a Primary class for children. The purpose of the rings (or necklaces, etc.) is to help inspire those who wear them to make correct choices, consistent with the gospel values that they have been taught. Today, many Latter-day Saints (including adults) wear CTR jewelry. Unlike temple garments which should only be worn by endowed Latter-day Saints due to their religious meaning, CTR rings are a cultural item associated with the Church, and are therefore appropriately worn by anyone wishing to "Choose the Right".
They must consider wearing a cross is "Choosing the Wrong"
The “official” explanation is: “Latter-day Saints do not use the symbol of the cross in their architecture or in their chapels. They, like the earliest Christians, are reluctant to display the cross because they view the “good news” of the gospel as Christ’s resurrection more than his crucifixion.”
The LDS also believe that the Atonement of Christ took place in the Garden of Gethsemane not on the Cross. The point of the Cross was not the shedding of his righteous blood for sinners but the fact He HAD to die, in order to be resurrected, not to prove He was the Son of God, but so we could all be resurrected.
Mormon use of the term “salvation” refers to the resurrection of all people, not spending Eternity in the presence of God (LDS use the term “exaltation” for that).
I wear a Cross for very personal reasons, it is a constant reminder of Whose I am, and that it cost the precious blood of the innocent Son of God to purchase me. I wear a Cross to be reminded of what Jesus went through for me (and for you and for everyone else).
I wear an empty cross (not a crucifix) becuase Jesus is NOT STILL ON THE CROSS. HE IS RISEN!!