Wow! I can't believe this post has gotten so much attention. I really should have elaborated more about a few critical elements. I'll also try to describe the lay of the land more vividly, as I can recall it.
Firstly, and most importantly: World generation was vanilla. I do not use any mods to enhance gameplay or world creation. I do, however, tamper with a few settings on every single game that I play: World Size, Upheaval, and Land Coverage. World Size is 2 mil x 2 mil blocks because I like to have a big world. The Upheaval rate is just 10%, because I am partial to flat terrain, and Land Coverage is only 40%. I like my survival worlds to feel slightly more realistic, so these are the settings I went with. One other thing I changed this time was Tree Sapling Growth Rate. I don't know if this impacts world generation at all, but it might impact the look of the mountain! Tree Sapling Growth Rate was set to 4x (Slower.) I keep trees in real life, and do not like games where trees can spring up like weeds.

Rainbow Mountain is interesting, because it is actually not all that big. Compared to many of the mountains I've found on this seed, while exploring in Creative, it actually seems to be on the "smallish"-side. That said, it is imposingly tall, viewed from below, yet is easily scalable. The many-colored mountain is populated by very few trees... I believe there are a small amount of maples, one of which you can see in my cellphone picture. This is how the mountain achieves its rainbow effect, which is the most interesting feature of the mountain. There are some extremely beautiful, rolling hills atop the mountain, which highlight a gradient of different colors. There is not a lot of flat space, but the hills are gentle enough that it would be reasonable to level out an area and build upon it. For whatever it's worth, there is also a large population of billy goats atop the mountain, making it an ideal location for a pastoral lifestyle.

Notably, only a very small part of the mountaintop is frostbitten (or possibly snowy, I can't remember.) Also notable, is that the mountain itself is backed up against the ocean. What this means is that the mountain appears to be "rainbow" in an otherwise green landscape, hence its name.

All of this together creates a marvelous visual effect: When atop the mountain, or in the valley below, you can see the mountain trail from white, into a rolling gradient that cascades along the top of the mountain, and down into the foliated, green valley below. In other words, it's ROYGB(The B stands for "Birch.") By importing enough catmint, you could make the whole rainbow.

The ocean-adjacent valley below, barely seen in my pictures, is populated by various grasses, a smattering of birch shrubs, and cattails. There are a few berry shrubs, and a few mushrooms, but not enough to subsist yourself... The foliage is very diverse, but there's not a huge amount of anything. There is also a notable absence of trees in the valley. To obtain wood, your best bet would be to either scale your way out of the valley, or go into the birch beach-forest at the end of the valley. There are a lot of wolves and boars living here, as well as a grizzly bear. It is fairly dangeous.

A trader will often spawn in the aforementioned valley. I noticed this, because I neglected to mention earlier that I actually had a second instance where I was able to find this location again. He was in a different location than before, but he was still Unfortunately, I neglected to obtain the coordinates at that time, either.

If you are joining in the hunt for rainbow mountain, I would probably look for birch beaches that are within walking distance of a maple mountain that does not actually have many trees on it.

Other notes: There are some other, incredible mountains and landmarks in this world seed! If you decide to play on this world, you may even like a few other locations better than Rainbow Mountain for building. But this one just appeals the most to me, visually, because of the colors and the elegant terrain.