The horse-lords' country south of Fangorn is Rohan.
Rohan is the inland kingdom of the Rohirrim, the horsemen whose cavalry repeatedly comes to Gondor's aid. Fangorn Forest borders Rohan to the north, while the White Mountains lie to its south. Its capital is Edoras, where King Théoden rules from Meduseld, the Golden Hall.
Tolkien shaped Rohan's language, names, and culture around Anglo-Saxon England, especially the historical kingdom of Mercia. The Rohirrim call their land the Mark or Riddermark, and their famous horses include the exceptionally swift mearas. Rohan's history is closely tied to Gondor through the Oath of Éorl, a promise of military assistance in times of danger.
A common mix-up is confusing Rohan with Gondor. Gondor is the southern realm of Men, centered on Minas Tirith; Rohan is its northern ally and is best known for mounted warriors. Rohan also includes Helm's Deep and the Gap of Rohan, important locations during Saruman's invasion.