As Jane said blue eyes are caused by Splashed White or Frame, but horses with those patterns don't necessarily have blue eyes themselves and their parents may not have blue eyes either. This isn't a case of the white marking gene being recessive, the gene is just minimally expressed. Many minimally marked Splash or Frame horses have brown eyes, but they reproduce blue eyes in their offspring. Appaloosa patterns alone don't cause blue eyes, they must be combined with either Splash or Frame. Many full sized Appaloosas, especially the Bright Eyes line, are Splash.