Blue eyes are also seen on double dilutes. Single dilutes - buckskins and palominos - often still have brown eyes, but they are lighter in color.
The champagne gene turns the eye blue-green at birth and hazel or amber at maturity. Paso Fino horses also carry a gene that produces an amber eye.
Green eyes are extremely rare in horses. They are found in horses that carry the pearl gene (a rare dilute gene) and very, very rarely on homozygous cream or cream and champagne - but in all these instances the eye is more commonly blue, amber, or hazel.
Normal brown eye (source AnemoneProjectors via Wikimedia Commons).
Blue eye on a paint horse (Source: Kalike via Wikimedia Commons).