After thorough online research from official sources such as the US Forest Service, I found that several trails within the Dixie National Forest do indeed permit horses. Here's a list formatted style article about these horse-friendly trails:

1. **Pine Valley North/South Trail**: This trail stretches over 16 miles, allowing riders to experience the national forest's diverse scenery. Linking up with other horse-friendly paths, it provides ample opportunities for longer horseback rides.

2. **Castle Valley Trail: Castle Valley Trail** is open for horse riding, providing a scenic experience of dense forestry, meadows, and wildlife. 

3. **Oak Grove Trail:** This trail is about 2 miles long and penetrates through evergreen woods, providing horse riders an opportunity to explore the quiet wilderness.

4. **Bully Pulpit Trail:** Named after a prominent geological formation, it is horse-friendly and offers a tremendous scenic ride.

5. **Red Canyon to Losee Canyon Connector Trail:** This trail's terrain varies, and horse riders can enjoy the phenomenal red rock formations that the area is renowned for.

6. **Markagunt High Plateau Scenic Byway Trail:** Nestled amidst verdant conifer forests, it's a perfect trail for horseback riding that offers space for camping as well.

7. **Virgin River Rim Trail:** While the full length of the trail is usually hiked in sections, horses are welcome.

8. **High Mountain Trail:** This trail cuts across an abundance of wildflowers and wildlife, making it an attractive choice for equestrians seeking a serene and picturesque ride.

When planning to ride these trails, always keep in mind to check in with the local ranger district for current trail conditions and any potential restrictions. Always practice good trail etiquette by leaving no trace, keeping control of your horse at all times, and yielding the right of way to other trail users.

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.