Given some of the comments in this question, I feel compelled to ask: "Does Mormonism constitute a present-day example of a mystery religion?" I'm interested in both insider and outsider perspectives.
The article states that Christianity itself, particularly as it originally existed in the days of the early Church, meets the definition of a mystery religion, and that this was noted and remarked upon by one of the great early apologists, Justin Martyr. And if the definition is that "participation is reserved to initiates," then Judaism meets the definition as well: Gentiles who had not converted could not take part in many of its sacred rituals, particularly ones that involved the Temple. The Temple had an outer area known as the court of the Gentiles where outsiders could come, but beyond that, they were not welcome.
The Church of Jesus Christ of Latter-Day Saints claims to be the restoration of original Christianity, so it's not surprising to see such features as part of its theology. Participation in sacred temple ordinances is "reserved to initiates," as the article describes it, and certain matters regarding temple ceremonies are not to be discussed outside of the temple.
However, there is an important distinction to understand: to Latter-Day Saints, these matters are not secret; they are sacred. I explained the difference in this question: the value of a secret is in exclusivity, whereas Latter-Day Saints actively invite and work to persuade all to come to the temple, but only once certain standards of preparedness, understanding, and spiritual maturity have been met.
Forgive me for commenting over a year after the question was asked. I am a Mormon, and I consider myself to be passionate not only for my own faith, but for religion in general. My current religious obsession is in the Greco-Roman mystery religions, particularly those claiming authority from Orpheus. The more I learn of these faith traditions, the more I'm staggered by the similarities I see in my own faith. In the LDS temples, as in the mystery ceremonies of old, we make oaths and promises to ensure a good afterlife, we are sworn to secrecy (to a degree), and we learn sacred tokens, passwords, and instructions for use after our physical death. One major difference between ancient mystery cults and Mormonism is that, though we are threatened by spiritual damnation for revealing our temple practices, we are not under threat of death for doing so. Those who have no fear of damnation have revealed the aesthetic layer of our practices, and so the respectful silence of the ancient cults has sadly eluded us.
It's not necessary to attend the temple or participate in temple ordinances in order to belong to the LDS church. One merely needs to be baptized by someone holding the Aaronic priesthood to be considered a Mormon. Temple ceremonies are completely optional, and (ideally) dependent on personal worthiness. For these reasons, I would say that Mormonism is similar to the ancient mystery religions, but isn't necessarily a mystery religion itself.