Step 1: Understanding horse evolution.
The evolutionary history of the horse shows a clear progression from small, multi-toed forest dwellers to larger, single-toed grazers adapted to open grasslands. Each genus represents a stage in this evolutionary transition.
Step 2: Geological time sequence of the genera.
- Orohippus (Eocene, about 50 million years ago): One of the earliest horse genera, evolved soon after \textit{Eohippus} (Hyracotherium). It had four toes on the front feet and three on the hind.
- Mesohippus (Oligocene, about 37–32 million years ago): Slightly larger, three-toed horse, adapted to more open woodland.
- Merychippus (Miocene, about 17 million years ago): A grassland horse, three-toed but with the central toe dominant, an ancestor to modern horses.
- Pliohippus (Miocene–Pliocene, about 12–5 million years ago): First true one-toed horse, close to the ancestor of modern \textit{Equus}.
Step 3: Determining the oldest genus.
Among the given options, Orohippus belongs to the \textit{Eocene epoch}, making it the oldest genus listed.
\[
\boxed{\text{Orohippus is the oldest horse genus.}}
\]