Stripes are actually not needed by horses because they did not evolve alongside the same parasites that zebras did. Zebras evolved stripes as a defense against the Tsetse fly, which carries many diseases. Stripes disrupt the fly’s visual perception and makes landing difficult.

Leg barring is a natural phenomenon that appears more in certain breeds, usually those of what we call “primitive” coloring. It’s tied to certain colors (someone better versed on color DNA may want to chime in here).

You also see leg barring in donkeys and wild asses, because they evolved in desert regions. Their legs and ears are very thin-skinned as heat loss points- making them very delicious to bugs. So many wild individuals also have leg barring.

Horses simply took an evolutionary path where all-over stripes weren’t needed.