The better the horse's genetics are, the more stars it will have. I know it's more complicated than that but I can't find any documentation either.

registered pure horses will receive yellow stars - the more yellow stars, the better BV a horse has. 

grade horses receive purple stars

Crossbred campaign horses have teal stars 

Unregistered crossbreed get grey stars.

Thank you for the explanation on the colors! I had noticed some of the different colors but hadn't picked up on the pattern. ^_^

@ERA

I don't have a single grade horse with purple stars, they've all grey stars. Any idea why? ?.?

I think purple stars are for registered/recognized crossbreeds. All my Drum Horses have purple stars.

That would make sense! Thank you!