What is the origin of the moral-civil-ceremonial distinction of the Old Testament law? This distinction is often called tripartite division of the law.

I ran across this series of blog posts, which considers the division of the law into "moral", "civil", and "ceremonial" parts:


Introduction 
Historical Overview 
Analyzing Aquinas' arguments 
Analyzing Calvins' arguments 
Wrapping up with two more historical views 
Entertain generic arguments for flaws in the tripartite assumption 
Some final thoughts 


The Westminster standards (and others), even go on to claim that the "moral" law is one and the same with the Ten Commandments. This sometimes becomes something of a hermeneutical key, e.g., when interpreting passages that point out that the law is overturned, asserting that the passage is referring to the ceremonial law. 

That said, Confessional Presbyterians and Reformed Baptists are not typically considered Thomists, and yet find this principle as no minor point in their confessional documents. Aquinas's reasoning is usually rejected when directly addressed, but the essential division is held nonetheless. Is there some other supporting reasoning, or an alternative origin other than via Aquinas? Likewise, is there support for equating the "moral law" (which is said to remain on Christians) with the Decalogue?
You can look at the Catechism of the Catholic Church for more information about equating the moral law with the Ten Commandments.

Here you can read a nice summary of this section. But, to break it up into some parts to help explain, you may want to look at the definition of a moral law:


1950 The moral law is the work of divine Wisdom. Its biblical meaning
can be defined as fatherly instruction, God's pedagogy. It prescribes
for man the ways, the rules of conduct that lead to the promised
beatitude; it proscribes the ways of evil which turn him away from
God and his love. It is at once firm in its precepts and, in its
promises, worthy of love.
1952 There are different expressions of the moral law, all of them
interrelated: eternal law - the source, in God, of all law; natural
law; revealed law, comprising the Old Law and the New Law, or Law of
the Gospel; finally, civil and ecclesiastical laws.
1953 The moral law finds its fullness and its unity in Christ. Jesus
Christ is in person the way of perfection. He is the end of the law,
for only he teaches and bestows the justice of God: "For Christ is
the end of the law, that every one who has faith may be justified."


So, the first stage of revealed law is the Ten Commandments, but these were perfected by the New Law (the grace of the Holy Spirit), so we can see by the CCC that moral law is more than just the Ten Commandments, but, also covers the New Law.

Now, as much as I am a huge fan of Aquinas, I tend to think that there can be problems with his divisions, but they can also be useful for explanation, but the problems should also be understood.

This article does a good job of explaining problems with dividing them.

We should not decide which is critical to obey and which can be ignored, safely.  I like this quote from the link above:


  If God says it, it is immoral to disobey. Morality is not a standard independent of God. God decides what is right and what is wrong.


Here is a likely reason for the three-part division, taken from this historical background:


  Why were the dogmatical terms of Moral, Civil and Ceremonial developed
  if there is no division in the Bible and the Jews never considered the
  Law as threefold? The division probably was developed because there
  are 3 natural parts to the Mosaic Law. It also makes for easier
  teaching when we study the Old Testament Law in a threefold sense. The
  Law of Moses is massive in scope.


So, you are correct that it appears to have started with Aquinas, as far as I can tell, but there does seem to be a natural split of the Law into two parts, a moral and ceremonial, as well.