The one is yellow, as is the nine. The two and ten are blue, are and so on. These colors are standard—anyone who has played pool for even a short time doesn’t need to see the number on a ball to know what it is, whether they’re playing in New York, California, or Canada (assuming they’re looking at a pocket billiards table, not snooker or some other game).
Who/what body decided on this standard color arrangement?
Definitely not the people who created snooker…a pink ball? Just stop it.
Maybe it just happened.
In Britain, the only numbered ball on every pool table I ever played on is the black 8 ball. The other balls are red & yellow, no numbers.
So no 9-Ball for you then?
That’s a British 8-ball set. Seven reds, seven yellows, an eight and a cue-ball. It’s extraordinarily stupid since you can’t play any other game with it.
On reflection, there are people playing crazy games on pool tables whenever I go to a snooker club. But I never really took much notice of them, the tiny-tabled heathens.
I play pool drunk in the pub & playing a variation with different coloured balls would be plain confusing.
The first attempt to standardize pool ball colors was by Sir Roderick Billiard in 1892. Sir Roderick’s game included a cue ball numbered zero (0), a pink #2 solid, and red felt on the table.
The changes to today’s solid white cue, blue #2, and green felt were instituted by the Ernest L. Brunswick Co. of Camden, NJ. in 1917. Red felt was being used to line the boots of USAF pilots, and Brunswick could only procure blue or green. Green won out. Brunswick had called the pink #2 a sissy color, and despite the pre-existence of a blue striped #10 ball, Brunswick decided that two blue balls would not cause a problem.
I suspect at least the first paragraph of your post may be a whoosh, but while we are fingering the founding fathers of our beloved cue sports, I have to apologise in advance for a slight hijack.
Snooker as we know it was invented by Neville Chamberlain, a relative of the more famous Neville Chamberlain. There was also a third Neville Chamberlain of some note in the family. They are all cousins of Alan Napier, who played Alfred in the Batman TV series.
Hijack over. Who knows about the pool ball colours?
The colors have changed in recent years to accomodate television. The four ball has changed from blue to pink so it wouldn’t be confused with other dark colored balls, for example.
And I’ve seen 8-ball sets with every conceivable color combination. About the only absolute standard you see is a white cue ball and a black 8-ball. But even the cueball is changing - now you often see it with various lines and markings on it so that spectactors can see the spin applied.
That has not been my experience, however. 
That’s all well and good, as are British or other games’ color (colour) conventions. But be that as it may, you can go to just about any bar with a table (and one that doesn’t serve froofy overpriced pseudo-martinis) and tell that the yellow striped ball is a nine, the solid orange ball is a five, and so on.
Somebody must have devised and standardized this schema, whether it was a manufacturer, a pool hall, a player, Xenu, or perhaps … Cecil.
It really depends on how cold the pool is.
…says someone with Alaska for a location 
The thermometer on the shady side of my construction trailer says -22F. On the sunny side, it says -15F. Woo-hoo; think I’ll run out and take a dip.