A palomino is a particularly popular kind of horse, with a coat color that ranges from almost white to golden yellow.
If you've dreamed since you were little of riding a palomino along a deserted beach, it means that you picture yourself on a pale golden horse. Palominos turn up in movies, parades, and shows because they're unusual and considered to be particularly beautiful. Mr. Ed, possibly the most famous television horse, was a palomino. The word palomino is Spanish, and it means (oddly enough) "young dove."