It is going to depend on the discipline, since to a great degree that determines the breed of horse, and certain colours don’t occur in all breeds.
The cream dilute genes (which cause palomino and buckskin), roan gene, and dun factor are much more common in quarterhorses and mustangs, while the cream dilutes, roans, and some fun stuff like chocolate palomino and chocolate dapple turn up in some of the gaited breeds. Also the pinto patterns, in both stock horses and gaited horses. So if you were in a western barn or a saddleseat barn, you’d probably get a higher percentage of these colours. Plus of course appaloosas in Western.
Some on-line photo albums of self-contained or isolated mustang herds show almost an entire herd is cream dilute, buckskins and palominos. Maybe it’s a survival advantage in the desert?
If you were in a hunter/jumper or dressage barn, your thoroughbreds would be black, bay, chestnut, and grey primarily. Your warmbloods the same, but there are a few lines with pinto (tobiano, sabino, or splash; frame overo mutated in North America, out of Spanish horses, so wouldn’t occur in any true European breed, and is most common in Quarterhorse Paints and mustangs). If you were doing dressage with Ilberian horses or Lipizanners, though, grey would definitely be over-represented.
And purebred Arabians cannot be palomino, or pinto, though some very “typey” cross breeds exist in these colours, usually through mixing to quarter horses or paints a few generations back.
But it is also true that all this coat variation reduces to base coat colour of either black (bay is a variation of black) or chestnut, with the various colour modifiers working on those (cream, roan, greying out, chocolate dapple, pinto, appaloosa, etc).