What does Paul mean by "divine nature", as revealed through creation?

You may not be "particularly interested" in this Answer, because it is not expressing "evangelical (or more generally reformed) views", but I will provide it anyway, because it is philologically sound.

The word θειότης is used only once (in Rom 1:20) throughout the NT. I believe that the English "divine nature" more than a translation is a metaphysical interpretation.

Only with a Thomistic approach can one believe that we can move from Creation to the "divine nature" of the Creator. We can, at best, say that what we can perceive in Creation as θειότης is God's power, so I propose this equivalence:

θειότης (Rom 1:20) = θεία δύναμις (2 Pet 1:3 - NOT θεία φύσις - 2 Pet 1:4)

More, I believe that δύναμις καὶ θειότης at Rom 1:20 is a hendiadys for θεία δύναμις

What does Paul mean by “divine nature”, as revealed through creation?

For since the creation of the world God’s invisible qualities—his eternal power and divine nature—have been clearly seen, being understood from what has been made, so that people are without excuse. - Romans 1:20

But what does Romans 1:20 mean?

According to the previous verses, those who are unrighteous before God do not want to know about Him, so they try to suppress the truth about God. To some extent, this is true of all human beings, since we all sin (Romans 3:23). Paul has shown that God has plainly shown what is knowable about Him to everyone (Romans 1:18–19). How has He done that? This verse answers that it is obvious from what He has made.

Specifically, Paul asserts that human beings can easily know at least some things about God by looking at creation. We should look at what is visible around us in nature, what God has made, and arrive at some obvious conclusions about what is not visible. Adding one and one together, we should understand from nature that God has eternal power and a divine nature. David said something similar in Psalm 19:1–6.

After all, Paul seems to be saying, what kind of power would it take to make the world and all that is in it? Such a feat would require "eternal power," or endless and inexhaustible power. Such a Creator must also be divine and not merely human. He must be God, in other words. Human beings should look at creation and decide there must be a God who made it, a God we must answer to on some level.

Especially in our era, some might argue that reaching such a conclusion by looking at nature is not a given. After all, the prevailing alternative theories about the origins of our universe may lead someone to decide that just the opposite is true: There is no God. God does not accept that argument. This passage is especially important when viewed in context with Jesus' comments in Matthew 7:7–8. God gives every single person enough knowledge that they should seek Him. Those who respond by seeking God will always find Him.

If human beings do not "work out" the basic nature of God from what is seen in creation, and seek Him from there, they are simply "without excuse." They are willfully ignoring the obvious. God insists that He has made it plain to human reasoning and that to decide otherwise is to suppress the truth we know by nature.

St. Thomas Aquinas has a great explication on this and I would recommend it here (The Divine Nature). Not all reformation churches disagree with St. Thomas and some even hold him in high esteem.

• Thomas Aquinas: Not Just for Catholics Any More
• Did reformation leaders throw out the Summa Theologica?

God's revelation of himself through creation has been clear [...] The truth that Paul says is being suppressed is Genesis 1:1: "In the beginning God created the heavens and the earth."

(Source)

The heavens declare the glory of God,
and the sky above proclaims his handiwork.

(Psalm 19:1, ESV)

To understand what is revealed, we must first understand the nature of the revelation. To that end, Romans 1:19-20 is a direct rebuttal of Methodological Naturalism, which is rampant in "science" today. (When you approach science from a dogmatic rejection of certain possibilities, such as the possibility that God exists, you are no longer engaged in real science.)

To quote the quote from Ken's answer:

Those who are unrighteous before God [...] try to suppress the truth about God [...] They are willfully ignoring the obvious. God insists that He has made it plain to human reasoning and that to decide otherwise is to suppress the truth we know by nature.

...and:

We should look at what is visible around us in nature, what God has made, and arrive at some obvious conclusions about what is not visible.

An impartial consideration of our world clearly reveals that we aren't here by accident; that Uniformitarianism, and especially Evolutionism, are errors which can exist only by willfully suppressing what God has made plain and obvious. Naturalism is inadequate to explain Creation, or our existence. This is "clearly seen, being understood from what has been made", and those that deny this truth are "without excuse".

It's important to understand this, not just for the sake of understanding this passage as a whole, but because ultimately the answer to the question, at least in context, is that the "divine nature" of which Paul speaks is that nature necessary to accomplish Creation. This nature is therefore, at least in this context, defined by what it has accomplished. The clear testimony of Creation is that it defies a Naturalistic Cause. We are thus convicted to acknowledge the beauty and order inherent in Creation; attributes which are the product of an Intelligent Designer. The "divine nature" thus revealed is that some entity — that is, God — possess the ability to bring about such a Creation. And indeed, it is this nature, and this act of Creation, which are plainly attested in Genesis.

Thus, one answer I could give you is that if you wish to understand God's Divine Nature, at least as expressed in Romans 1:20 specifically, you should become a scientist! (Albeit, a real scientist; one who accepts the possibility that God exists, not a so-called "scientist" who dogmatically rejects that possibility.) The more you understand about what God has created, the more you will understand what Nature He must possess in order to have accomplished such Creation. Of course, if that sounds like too much work, you could also just sit in a park and (re)read Genesis 1 🙂.

I don't know what specific "notable leaders" in theology hold such views. I can say that Martin Luther — generally regarded as the "father" of the reformed/evangelical faiths you (OP) asked about — did not reject the plain Genesis account (see here and here). I know that at least some reformed/evangelical denominations have not surrendered to the anti-theistic, anti-biblical pressures of Naturalism (and the religions of Uniformitarianism and Evolutionism which flow out of it). I know that there are organizations, such as Answers in Genesis, Creation Ministries, International and the Institute for Creation Research that also hold this stance. Many individual Christians also accept these biblical truths even if congregations and denominations consider them "inconsequential" or fail to preach them. (But these questions are far from inconsequential! Naturalism is nothing less than the explicit denial of God. Uniformitarianism denies historical teaching of the Bible. Evolutionism in particular undermines the very foundations of Christianity.)

Okay, but what is God's Divine Nature? Again, the short answer is "that nature necessary to accomplish Creation". The entirety of (real) science could be said to study what that nature can do (and has done!), but it may be that a more complete comprehension of such a nature is simply beyond our abilities. Still, you could read this and this for some other statements of this generality.

The best answer I've managed to find, however, comes from AIG, which is that God:

• ...is eternal. God exists outside of what we know as time. He was before Creation, and He will be after it is gone.
• ...is powerful. He created and sustains the universe, and us.
• ...has a mind and a will. Creation isn't haphazard, nor did it come into existence by itself; it was designed, and, further, was designed with great beauty and diversity. There is also great order in nature.
• ...is moral. He created humans with a conscious that guides and convicts us.
• ...is loving. He created a world which sustains us and provides resources that enable us humans to grow and thrive, not just physically, but as a technological civilization.
• ...is just. Death and disease attest to the consequences of sin. Geology and fossils attest to the judgement of the Flood.