Joseph Smith speaks of those who have "tasted of the powers of the world to come". Note that this says "tasted of the powers". It wasn't a matter of seeing things to come. It wasn't a matter of knowing of things to come. They tasted of the powers of the world to come.
And how so?
We see this clearly in Moses 1, for example. The glory of the Lord is upon Moses and Moses can perceive the world as God can, to a degree. He can perceive every individual. At another point he can perceive every particle of it. The glory of God is the light of Christ that proceeds forth from the presence of God to fill the immensity of space and is the means by which he is in and through all things and governs (i.e. has power over) all things. When God's glory was upon Moses, Moses tasted a bit of what that power is like. Experiencing this is what he referred to when he said something like "Now I see that man is nothing, which thing I never had supposed." He has seen that the glory by which God controls and sees all things is something his own mortal body cannot even endure without being transfigured. He has seen that without a better body, he cannot become like the Father, because his mortal frame cannot endure the eternal glory.
Thus Moses didn't just "learn about the powers of heaven", Moses "tasted the powers of the world to come" as did many others. He experienced a taste of them.