Of the dozens of possible horse treks, several are popular and not difficult to arrange.
The most popular horse-trekking area is khovsgol Nuur, largely because there is such a good network of guides and available horses. Some travellers have horse-trekked from Terkhiin Tsagaan Nuur to Khovsgol Nuur. By land (following the twisting river valleys) it’s around 295km and takes at least two weeks! by horse.
Tsetserleg to Bayankhongor is a rugged wilderness trip that crosses a series of alpine passes.
In the east, try the Binder area of Khentii aimag, which can include a ride to Dadal near the Siberian border.
Closer to Ulaanbaatar, the areas of Terelj and Bogdkhan are both excellent if you don’t have a lot of time.
In western Mongolia there is great horse trekking around Otgon Tenger Uul; it can take six days to circle the mountain.
In Altai Tavan Bogd National Park, try a horse trek around Khoton Nuur. There is also horse trekking around Tsast Uul and Tsambagarav Uul. Tour operators in Olgii can help set something up, or just turn up in any nearby village and ask around for horses.