According to Catholicism, did Moses believe in the Trinity?

Moses believed in the Trinity. The real question is when he came to that belief. In the story of the Transfiguration, we hear this:

30 Two men, Moses and Elijah, appeared in glorious splendor, talking with Jesus. 31 They spoke about his departure, which he was about to bring to fulfillment at Jerusalem. (Luke 9:30-31)

About the nature and depth of the relationship between Moses and God, we have this:

The Lord would speak to Moses face to face, as one speaks to a friend. Then Moses would return to the camp, but his young aide Joshua son of Nun did not leave the tent. (Exodus 33:11)

Then later in Deuteronomy 34:

10 Since then, no prophet has risen in Israel like Moses, whom the Lord knew face to face, 11 who did all those signs and wonders the Lord sent him to do in Egypt—to Pharaoh and to all his officials and to his whole land. 12 For no one has ever shown the mighty power or performed the awesome deeds that Moses did in the sight of all Israel.

We know that God told Daniel and the Apostle John things that were not to be shared with the world but instead be sealed up. We can infer that Moses knew God in a way that no one else did and that at least by the time of the Transfiguration Moses knew of the triune nature of God, if not during his prior life.

In the above quotes, the key phrase is about his departure. Since God told Moses things plainly - not in parables as he did with the disciples and many other prophets - then he told him plainly about his departure, which consists in:

• Crucifixion and death as a sacrifice
• Resurrection
• Ascension into Heaven

Those events identify Jesus as divine.

In Exodus through Deuteronomy, Moses was called four times. Each calling was significant and was attended by an important new revelation. There were five main sacrifices, five Books of Moses and other reasons suggest that there ought to have been five callings, the last for fulfillment, a great harvest, entry into the Promised land and peace. Moses died before the fifth call. The Transfiguration was his fifth call, when Moses finally entered the Promised Land, setting foot on the Holy mountain, at last inside the borders of Israel. Surely this meeting of Jesus and Moses would be the greatest, when Jesus would bestow knowledge beyond what he had already received.

Moses recognized the incomprehensiblity of God in this life. He knew of the UNITY of God but that unity is many many things in the history of thought about God It does not in any way exclude a Trinity of Persons. The Catholic definition is " the unity of Father, Son, and Holy Spirit as three persons in one Godhead"

No, Catholicism does not assert that Moses believed in the Trinity as such, although obviously he believed in the One God, and if that One God is Trinitarian in nature, he believed in the Trinity in an indirect, obscured sense.

As the Catholic Encyclopedia article The Blessed Trinity summarizes in the section 'Proof of Doctrine from Scripture, B. Old Testament',

"The matter seems to be correctly summed up by Epiphanius, when he says: "The One Godhead is above all declared by Moses, and the twofold personality (of Father and Son ) is strenuously asserted by the Prophets. The Trinity is made known by the Gospel" ("Haer.", lxxiv)."

However,

"The early Fathers were persuaded that indications of the doctrine of the Trinity must exist in the Old Testament and they found such indications in not a few passages. Many of them not merely believed that the Prophets had testified of it, they held that it had been made known even to the Patriarchs."

That some early Church Fathers believed something does not mean the Catholic Church holds it. As the article goes on to say,

"But in others of the Fathers is found what would appear to be the sounder view, that no distinct intimation of the doctrine was given under the Old Covenant."

Continuing,

"Some of these, however, admitted that a knowledge of the mystery was granted to the Prophets and saints of the Old Dispensation (Epiphanius, "Haer.", viii, 5; Cyril of Alexandria, "Con. Julian.," I). [...] Yet it seems that the Gospel revelation was needed to render the full meaning of the passages clear. Even these exalted titles did not lead the Jews to recognize that the Saviour to come was to be none other than God Himself."