JOEL - There were many early church leaders who were members of the masonic fraternity, especially during the Illinois time period and as they began moving into Utah. However, because of the moral outrage felt by other Masons over the issue of polygamy, Grand Lodges in both Nevada and Utah banned Mormons from Masonic membership for several decades.
But later, after the Church discontinued polygamy and raised itself in popularity and esteem, the bans imposed by Freemasonry were reexamined, particularly in light of the fact that no candidate for Freemasonry should ever be judged based solely on his religious affiliation. In 1984 a resolution was presented to eliminate the prohibition, and make members of the LDS church eligible to join and visit Utah Masonic Lodges.
There are a number of active church members today who are also masons, but not many. There has never been a general statement by the Church specifically discouraging its members from joining the Masonic Fraternity.
However, if you were to ask any one of the General Authority's advice about joining the Masons, they would probably advise against it. Church leaders caution that membership in fraternal organizations such as this should be avoided, because they may take time and energy available beyond your daily vocation and your hours of rest, that could be spent in furthering the interests of the church and priesthood and family duties..