After conducting an extensive search through the official website of the U.S. Forest Service and other resources, it has been confirmed that horseback riding is indeed allowed on specific trails in the Francis Marion and Sumter National Forests. Here, we have compiled a list containing the names of the trails that grant access to horses:

1. **Sewee Shell Ring Interpretive Trail**: This trail covers a distance of 2.3 miles and is part of the Francis Marion National Forest. The path is open for horseback riding, granting riders a scenic tour.

2. **Palmetto Trail**: Passing through the heart of Sumter National Forest, the Palmetto Trail welcomes horse riders along its lengthy route, stretching over 350 miles.

3. **Parson's Mountain Recreation Area**: Providing visitors with a diverse range of activities, Parsons Mountain Recreation Area is located within the Sumter National Forest and caters to horse riders with its specifically designed trails.

4. **Lynch's Woods Park and Nature Preserve**: Although this is not exactly within Sumter National Forest, it's managed by Newberry Parks, Recreation, and Tourism and is well-known for its equestrian-friendly trails. It's located nearby and often included in regional horse riding tours.

5. **Steed Creek Horse Trail**: A moderate-grade trail network with various loops in the Francis Marion National Forest. It has been specifically designated for horse riding.

Remember, while riding, horseback riders are urged to follow the trail guidelines to protect both the natural environment and the rider's safety. It's important to note that these are multi-use trails, so riders may encounter hikers, bikers, or wildlife along their journey.

Before starting your adventure, make sure to check the status of each trail, as closures may occur due to maintenance, inclement weather, or other factors. Check the U.S. Forest Service website or local park ranger stations for the most current information. Enjoy your ride!

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.