Big Hill Pond State Park in Tennessee offers a range of trails suitable for horseback riding. The park provides approximately 14 miles of equestrian trails which are primarily situated on old logging roads and park gravel roads. The trails designated for horse riding are marked with red blazes and are also referred to as fire roads. These fire roads are shared with mountain bikers, and it's imperative that horses stay on these designated trails and are not allowed on hiking trails or near the Lake Dam area.

One of the sources mentions a specific trail of 6 miles with an intermediate difficulty level, but does not provide the name of this trail. Horse riding in the park is restricted to day use only, with no overnight accommodations available for horses. Those wishing to ride must bring their own horses as the park doesn't provide horse rentals. 

The park's address is 1435 John Howell Rd, Pocahontas, TN 38061, and for further inquiries, you can contact the park office at 731-645-7967. For more detailed information about the specific trails, it might be helpful to contact the park directly or visit the park's website.

References:

1. Tennessee State Parks: https://tnstateparks.com/parks/big-hill-pond
2. TN Horse Trails: https://tnhorsetrails.com/