After thorough research, I found at least four trails in Fishlake National Forest that allow horseback riding. Please remember that while horses are allowed on these trails, riders should always ensure they obey rules and regulations related to trail use and minimize their impact on these beautiful natural areas.

1. **Mytoge Mountain Trail**: This interesting trail winds around Lake Fish in a loop and offers nice views of the surrounding environment. Its relatively flat terrain and easy accessibility make it ideal for a peaceful horse ride. 

2. **Fishlake Lakeshore Trail**: This is another circular trail that follows the perimeter of Fish Lake. It’s a slightly longer trail perfect for those who want to spend a few hours horseback riding. 

3. **Pelican Canyon Trail**: Horse riders often use this picturesque trail, which offers dramatic views of the area. Please be aware that some sections of the trail can be steep and require careful navigation.

4. **Oak Creek Trail**: This trail is another popular choice for equestrians. Riders will experience breathtaking views as they wind up towards Fish Lake.

Remember that horse riding rules should be properly adhered to while on these trails. Always make sure to check the trail status and conditions beforehand, as accessible trails are subject to change based on various factors such as the season and weather. 

Sources:

- official site of the U.S. Forest Service (https://www.fs.usda.gov/), 

- Trails website (https://www.trails.com/)

- Fishlake National Forest Brochure

- Utah Travel Industry website (https://travel.utah.gov/).

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.