Where can you do horse trekking in Kyrgyzstan?

Basically anywhere that one treks can be done as a horse trek, with a rare few exceptions like Ala-Kol where the primary trail is in parts either too steep or poor footing for horses. Most visitors will arrange these trips in tourist hubs like Karakol, Kochkor, Naryn, or Sary-Mogol; but in principle anyone with the language and horsemanship skills could arrange this directly with shepherds in the mountains.