Reading from left, for a standard pedigree: The horse's parents (sire, father, first, dam second) then each parent's parents (its grandparents) then each grandparent's parents, and so on.
Family trees for horses exist too and are used a lot in racing. One form starts with the name of a great horse, such as a Nijinksy, whose descendants have been very successful. it simply traces the line of his principal descendants down to the present. The purpose is usually to show that owner's horse is directly descended from a great one and has other close relatives which have been winners. Racing conveniently forgets descendants that win nothing (and there always plenty of those, whatever their sire achieved) .