I don't think Brigham ever felt it necessary to sneak around. He was a strict authoritarian and would simply issue orders--leastwise, that seems to have been the case with Zina Huntington and her husband Henry Jacobs. His other tactic was to teach that any woman was free to leave their husband for another man with greater priesthood power. I doubt it was any coincidence that Brigham happened to be the highest priesthood holder at the time.
I far as I am aware, after Nauvoo, BY was openly "sealed" to all his so-called wives. Unlike Joseph, I never recall having read anywhere of any BY secret relationships other than possibly the Nauvoo ones, but they were most likely unmarried. None of BYs "Celestial Marriages" were ever legal marriages. They were only sealings. One of Brigham's wives obtained a divorce and sued for alimony, but it was denied when Brigham's attorneys convinced the court that there had never been a legal marriage in the first place.
Almost all of Joseph's active sexual relationships with other men's wives occurred during the time between being caught in the Fanny Alger affair and his much later "sealings" to dozens of 15-20 year younger unmarried virgins. More than likely, Joseph probably had concluded that married women were a safer bet. They could easily explain a pregnancy and knew to keep the relationship secret. If ever questioned, Joseph could say that he was just visiting to comfort the wife of a devoted husband who was away serving the Lord on a mission. Being alone with a young girl would not be as easy to explain - especially to the ever inquisitive Emma.