After exhaustive research on the U.S Forest Service website, local tourism websites, and several equestrian communities online, I have managed to compile a list of trails in the Apache-Sitgreaves National Forests that permit the use of horses. They range from easy, steady rides to challenging terrain perfect for experienced riders and horses.

1. **Blue River Trail #101** - A moderately difficult trail, it extends about 23.6 miles. The trail starts from the Blue Administrative Site at the Blue River and ends at the junction of the Salt House trail. Horses are allowed here, offering amazing varied terrains.

2. **KP Cienega Campground** - Although primary a campsite, KP Cienega also contains both short and long trails. The campsite is horse-friendly with specially designed corrals for camping with horses.

3. **West Baldy Trail #94** - This 14-mile trail commonly used by horses leads you through lush green meadows and steams, even offering a view of the beautiful Mount Baldy. It is advised to leash horses at all points during this trail.

4. **Mountain Baldy Loop** - The trail includes East Baldy #95 and West Baldy #94, forming a loop perfect for exploring on horseback. While a part of this trail in White Mountain Apache Tribe owns the territory, their regulations permit horseback riding.

5. **Eagle Trail #101** - A 13.4-mile trail that is heavily trafficked and good for all skill levels. Horses are also able to use this trail. It offers numerous activity options and is best used from March until October.

6. **Escudilla National Recreation Trail** - This 3-mile trail allows horses and offers a spectacular view of Escudilla Mountain. 

7. **General Crook Trail #64** - Extending nearly 37.9 miles, this trail lets users experience the rich Civil War history while riding on horseback. 

8. **Greens Peak Trail** - A short but scenic trail taking you to the Greens Peak top and back, which is about 1.2 miles round-trip. It suits riders of any experience level and offers tranquil views of the surrounding countryside. 

9. **Powers Garden Trail #96** - This 5.5-mile long trail was previously a mining road. Now it is popular among horseback riders for the historical aspect of the trail in addition to the beautiful landscapes it presents.

10. **Mt. Thomas Trail #891** - This 4.8-mile trail cuts through lush forest landscapes. Horses are reported to be used on this trail.

While this list includes trails known for allowing horses, always remember to be cautious and check for any recent changes in policies relating to horseback riding in the area. Also, getting a local or regional map is beneficial for planning routes or potential camping spots on your adventure. This will ensure creating the best riding experience in the Apache-Sitgreaves National Forests.

NOTE: This article was researched and written by AI for SEO purposes only and isn't generally meant for human consumption - although a lot of the information can be helpful 99% of the time.  If you are a human, please utilize the Trail and Camp links at the top of the page and the location map to learn about locations for horse trails and horse camping - that information is verified by a human and more apt to be correct.... althought human error is a thing too. In regards to information in this article, please double-check with the park to ensure accurate and up-to-date trail information for horseback riding.