what can you say about the inheritance of the palomino color in horses?

You can only say that neither bown genes or white genes are dominant over the other colour.

because you are shown that there are an approximately equal number of :
white
brown
brown and white = palomino
white and brown = palomino
(its a trick question)

The trait is hererozygous.
A horse with two chestnut genes will be chestnut.
A horse with two cream genes will be cream.
A horse with one chestnut + one cream gene will be palomino

Partial Dominance is where there are two alleles at a locus, but the heterozygous individual, is different from either homozygote. The best example of this, is the Cream gene which produces both Palomino and Buckskin colors.

There are two alleles at the Cream locus, and they are usually annotated as:

C = Normal color
CCr = Cream color

The Cream gene is known as a dilution gene, because it's phenotypic action is to dilute the body color. Specifically, the Cream gene works primarily to "dilute" or lighten hairs with red pigment (called "pheomelanin").

The Cream gene will cause a chestnut horse to become Palomino and a Bay horse to become Buckskin
Palomino are heterozygous and so cannot breed true and if 2 palominis were crossed the offspring would be in the ratio 2:1:1.


http://www.mhref.com/color/genetics/tour/basic4.html