why me wrote:
I don't think that Joseph's polygamy was a big secret. He would usually ask the family members of the women involved for permission. That would include a lot of people knowing about the practice. Also, when his plural wives died and if they went west after his murder, their tombstone usually had the last name of Smith chiseled into them. However, given the persecution the saints were already experiencing and had experienced, the practice did have to be kept away from the general non-member public surrounding the Mormon community.
I think Joseph Smith wanted to keep it a secret. He denied the practice all the way to his death:
"I had not been married scarcely five minutes, and made one proclamation of the Gospel, before it was reported that I had seven wives. I mean to live and proclaim the truth as long as I can. This new holy prophet [William Law] has gone to Carthage and swore that I had told him that I was guilty of adultery. This spiritual wifeism! Why, a man does not speak or wink, for fear of being accused of this...I wish the grand jury would tell me who they are - whether it will be a curse or blessing to me. I am quite tired of the fools asking me...What a thing it is for a man to be accused of committing adultery, and having seven wives, when I can only find one. I am the same man, and as innocent as I was fourteen years ago; and I can prove them all perjurers." (Joseph Smith, History of the Church, Vol. 6, pp. 410-411) (From a sermon in 1844)
If he had been more open about the topic during his life maybe there would be less speclation about it.