There is a palomino breeders association in the US - not sure if they class it as a breed or not, but genetically, palominos are chestnut horses with one cream dilute gene - it is wholly colour and not breed related. Unfortunately even the palomino societies can be incredibly innaccurate about these horses at times. The following quotes are extracts from the palomino horse association.
"Many feel that Palomino is only a color and not a breed, which is true that the color of Palomino comes in all breeds, but the Palomino of Spanish times the Golden Dorado, was as close to being a breed as any strain of horse. The Dorado was of Arabic-Moorish-Spanish blood and breeding, closely akin to the Arabian and the Moorish Barb. The Palomino of Spanish times was not bred by being crossed with sorrels. The Spanish had many shades of golden horses, and when they did use "Corral Breeding" a light color Palomino mare would be mated with a very dark-colored Palomino stallion. This point has been noted in an old book and printed in Barcelona in 1774."
Ok, so if you want to take writings from 1774 as gospel, they bred palominos from palominos and got nothing but palomino. Genetically that's wholly innaccurate. There is only ever a 50% chance of getting palomino from pallomino x palomino - fact. So half the palominos they bred would have been palomino - the other half would have been sorrel (or chestnut) and cremello - obviously it wasn't noted what happened to them
. Another interesting point is that there is no cream gene in the Arab breed. Arabs don't carry that particular mutation. Any palomino you find advertised as Arabian will have had the cream introduced via another breed at some point in their breeding - so the Dorado was really a mongrel horse itself.
" In the last few years we have opened our doors to creme colored horse with blue eyes. It has been researched and proven that these light colored Palominos always produce a Palomino. Therefore, they are definite breeding stock for the Palomino. "
Or cremellos, as they in fact are. And yes, crossed with a chestnut they will indeed throw palomino every time, because they are chestnut with two cream genes themselves, so have to pass on cream when put to a chestnut and give palomino. However they will also throw buckskin, smoky black, perlino, smoky cream and cremello if put to a bay, black, smoky black, buckskin or palomino. So they are only definite breeding stock for palomino is used exclusively on chestnut mares. And the palomino offspring they produce still only have a 50% chance of passing on cream to their offspring.