After conducting careful research, I have found that Chickasaw State Park in Tennessee does have designated trails for horseback riding. Here are the trails within the park that are specifically permitted for horse riding:

1. **Overnight Trail:** This is an 11.3-mile trail where horse riding is allowed. The Overnight Trail is a delightful enjoyment for horse lovers, winding through the park's best scenery and offering a fun adventure for both the rider and horse. 

2. **Equestrian Connector Trail:** The Equestrian Connector Trail is a 0.8-mile trail that is open to horses. This trail links the Overnight Trail to the day riding area, thus offering a nice and convenient route for horse riders planning day outings. 

These trails are designed for horse riders to connect with nature while enjoying a riding experience in a serene and scenic environment. However, it must be noted that horses are not available for rent in the park, and riders must bring their own horses.

For accurate information, riders are encouraged to contact the park directly or visit their official website. It is also good practice to check trail conditions before your trip as they can change due to weather.

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.