The Hagerman Horse Fossil was designated the official state fossil of Idaho in 1988. 3.5 million year old sediments at the Hagerman Fossil Beds National Monument in Idaho contain the world's richest known fossil deposits from the late Pliocene epoch (200 horse skeletons have been recovered at the Hagerman Fossil Beds, 20 of which are complete).

The Hagerman horse (Plesippus shoshonensis, formerly called Equus simplicidens) is the oldest known representative of the modern horse genus Equus (includes horses, donkeys, and zebras) and is believed to be more closely related to the living Grevy's zebra in Africa than our modern horse.

Source:

State Emblems: Idaho Secretary of State
Hagerman Horse - Equus simplicidens: National Park Serv.
Hagerman Fossil Beds National Monument: NPS

Links:

State Fossils & Dinosaurs - 50 States