Did it have anything to do with their expertise and experience as Manchu horse archers, the period's guns and artillery as the decisive advantage needed to take the Steppes, population growth, or some other cause(s)?
EDIT: Title typo is kinda fortuitous. Knowing why the Qing did their conquering and how they went about it both would be most excellent, but if I had to choose one I would choose how.
Militarily yes. Guns combined with Manchu and Mongol cavalry made things easier.
We should note though that Qing suffered plenty of defeats.
Also both the Han and Tang controlled the steppe frontiers as well. So not all previous dynasties were unable to do so. Indeed Qing invoked a lot of Han and Tang legacies to justify their conquest.
All three ruled through client tribes instead of direct administration for Mongolia. The Tang and Qing presented themselves as the Great Khan and leader of a tribal confederacy instead of a foreign conqueror also helped (both had semi-nomadic roots). Same with Tibet, though Xinjiang is mixed for Qing. They also commit genocide on the Dzungar Oriats there, so there's that.
The plague effecting the nomads also helped.
I should point out since the Qing exercised control through client tribes, they didn't really wrestle control from the nomads. At least not until the period of the Great Game when they started implementing direct administration to counter Russian and British influences, though not in Mongolia I believe.