The question on whether Moses went to heaven is really a question about where all the Old Testament believers went after they died.
Heaven was not accessible to anyone before the crucifixion and death of Jesus. It is his sacrifice that opened the way for Christians and Catholics to go to heaven after they die.
So where did everyone before Jesus, including Moses, go? And where are they right now?
The first big question to answer is; where did Old Testament prophets, martyrs and believers go after they died?
It’s certainly not heaven.
Before Jesus, everyone who died went to the place of the dead or departed spirits. It’s called Hades or Sheol. Both the righteous and unrighteous souls ended up there.
But the parable of Lazarus in the New Testament indicates that the two groups were not lumped together. Here’s Luke 16:22-23.
The time came when the beggar died and the angels carried him to Abraham’s side. The rich man also died and was buried. In Hades, where he was in torment, he looked up and saw Abraham far away, with Lazarus by his side.
Lazarus went to a different part of Hades, the good part. This is referred to as Abraham’s Bosom and Christians believe that’s where pre-Christ believers went after death.
The fourth book of Maccabees gives us another clue on where the righteous ended up.
(4 Maccabees 13:17) For if we so die, Abraham and Isaac and Jacob will welcome us, and all the fathers will praise us.
So, no, Moses did not go to heaven after he died on Mount Nebo. He went to the good part of Hades, to Abraham’s Bosom.
That said, Moses is no longer in Hades.
Is Moses In Heaven Right Now?
When Jesus died, he did not immediately go to heaven. Instead, he descended into Hades. There he delivered all the righteous souls from Sheol. This includes Abraham, Jacob, Isaac, Moses and all other prophets and believers.
While the righteous had their own separate place in Sheol where they did not experience any torment, it still was not a good place.
Ecclesiastes 9:10 describes it thus;
Whatever your hand finds to do, do it with all your might, for in the realm of the dead, where you are going, there is neither working nor planning nor knowledge nor wisdom.
They also could not praise God as explained in Psalm 6:5.
Among the dead no one proclaims your name. Who praises you from the grave?
So Jesus had to go down and ransom their souls from the depths of darkness that is Hades. When he arose after three days, all the righteous souls from Hades went to heaven.
(Hebrews 11:39-40) These were all commended for their faith, yet none of them received what had been promised, since God had planned something better for us so that only together with us would they be made perfect.
In the new covenant, believers who die no longer go to Sheol. Instead, they are carried directly to heaven.
Right now, Moses and the righteous from the Old Testament are in heaven. One evidence of this comes from the transfiguration of Christ where Moses and Elijah appear alongside Jesus.
(Mathew 17:3) Just then there appeared before them Moses and Elijah, talking with Jesus.