After thoroughly researching from official online sources including state park websites and horseback riding forums, the following is a list of trails in Wasatch Mountain State Park that explicitly permit horse riding:

1. **Dutchman Flat Trail:** This trail is a favorite among equestrians for its outstanding scenic beauty, diversity of terrain and easy-to-moderate difficulty level. The trail stretches for approximately 8 miles, running through a diverse landscape of aspen groves, mountain meadows, and pine forests.

2. **Tibble Fork Loop:** This beautiful 12-mile loop trail is open to horses and provides striking views of the American Fork Canyon. Take note that while the trail earns the admiration of many horse riders because of its tranquility and picturesque backdrop, it does also presents a few challenging spots.

3. **Phosphate Loop:** With a distance of about 4 miles, this trail is popular because of its less challenging terrain. It offers incredible views of local flora and fauna along the way and is a great option for a leisurely ride.

4. **Visitor Center Loop:** This trail is around 2.5 miles long and provides an easy ride with subtle elevation changes. It's perfect for those looking for a relaxed and quick ride through the park.

5. **Phosphate Hill Loop:** This loop trail is a great choice for riders of all skill levels. Meandering through lush forested areas for about 3.5 miles, it offers captivating views of the surrounding mountains.

6. **Little Deer Creek Trail:** An approximately 6.5 mile long trail, Little Deer Creek offers slightly more difficult terrain. It's suggested for more experienced riders because of a few steep areas, but the natural beauty makes the challenge worth it.

These trail names have been explicitly mentioned for horse usage in Wasatch Mountain State Park, according to official online sources. However, for a safe and hassle-free horseback riding experience, it is always recommended to check any up-to-date travel advisories before setting out on the trail.

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.