Are Mormons Protestants? To my understanding, Mormons are neither Catholic nor Orthodox. I believe that they are Christians, but I'm not sure if they are Protestant or not.

Are Mormons Protestants, or are they just "Latter Day Saints"?
No, not really. While you sometimes find them lumped together they are not a subset of the class.

In popular usage such as among modern secular journalism, the term "Protestant" has come to mean anything that doesn't properly fall under the umbrella of either Catholicism or Orthodoxy. In this sense where there is no "Option D, none of the above", it sort of makes sense to lump in divergent sects with the rest of Protestantism.

There is, however, a fundamental difference: their theological roots are not the same. The LDS church is what is sometimes referred to as a "restorationist movement" — a reference to their theology's claim to be restoring something that was lost. While they agree with Protestants that the Catholic church lost its way, their proposed solution varies radically from that of Protestantism.

The basic tenets of Protestantism as a movement include rejection of a few Catholic doctrines and ultimately the Catholic church's claim to apostolic authority. In rejecting some of the core tenets of Catholicism, it based itself instead on a core set of doctrines (often loosely summarized in the "5 solas") that all require a certain reliance on the Scriptures as authoritative and uncorrupted.

The LDS church on the other hand is fundamentally based on the premise that Apostolic authority was lost (much earlier than even the rise of the Catholic church) and needed to be miraculously restored. This and other revelations are believed to have been given independently (and in opposition to) the existing claims of the Bible and historical Christian churches (whether Catholic, Protestant or Orthodox).

In other words, while they would also protest against Rome, their basis for doing so is entirely independent of the Protestant reformation and theologically they should be considered a sect (or cult depending on whose definitions you're using) outside of the theological umbrellas of Catholic, Orthodox, or Protestant traditions.