Psalm 90 is actually the only Psalm that has a sub-heading that identifies Moses as its writer (some Bibles do not include these) but it is fairly clear that his family was musical. Look at Exodus 15 even though Moses may not be credited with writing that song he did lead the Israelites in its singing and verse 21 Miriam follows his lead and starts playing the tambourine and dancing. He also leads (recites) a song in Deuteronomy 32 so he seems to at the very least have been a songwriter.  Over the years as I have read Psalms 90 through 100 I have wondered why most of them have no subtitles and that Psalm 101 is clearly marked as being written by David? The exception is Psalm 92, which is identified as being for the Sabbath Day. (possible placement of Psalms)

Ok, now for an active imagination because there is no proof for this other than contextual clues and some people may think that is a bit thin.  Look at the job that Moses actually had to do; teach the children of Israel about God after they had been in a pagan land for 400 years. They were more knowledgeable about Egyptian gods than they were about Yahweh just because they were around those demon gods’ art and statues. He had approximately one million people who knew very little about God that had to be instructed in His ways. What better way to do that than through song; so now read these Psalms as Sunday School lessons and focus on themes. Also, think about the trials and problems the Israelites had in Exodus through Deuteronomy.

• Psalm 90 – (think Exodus 15:26)
• Psalm 91 – (think Exodus 17:15) to make God your fortress and He will protect you
• Psalm 92 – (think Exodus 16:27)
• Psalm 93 – (think Deuteronomy 5,6) shifting thinking from Egyptian gods
• Psalm 94 – (think Exodus 10:29) a call for justice
• Psalm 95 – (a lesson after Meribah and sending out the first spies) exhortation to praise God and not tempt Him
• Psalm 96 – to praise God for His general judgments
• Psalm 97 – the majesty of God’s kingdom
• Psalm 98 – a general call to praise God
• Psalm 99 – the mercifulness of God and His right to reign (some sources suggest that it may not have been the Samuel of 1 Samuel)
• Psalm 100 – (think Exodus 40) giving praise to enter the new worship area

Thompson Chain-Reference Bible was a resource. NIV usually includes subtitles on Psalms.

Moses picture: http://www.google.com/imgres?imgurl=http://upload.wikimedia.org/wikipedia/commons/thumb/d/db/Moses_Pleading_with_Israel_(crop).