After careful online research, utilizing the Delaware Department of Agriculture website as well as other resources, I found that many trails in the Redden State Forest, Delaware, permit horse riding. Here’s the information verified from the official sources:

1. **Jester Tract Horse Trail**: This trail is horse-friendly and offers a peaceful journey through tall trees and diverse wildlife. It's important to note that the trail might be occasionally shared with hikers.

2. **Tussock Pond Nature Trail**: While primarily used for hiking and nature walks, this trail also opens up for horseback riding. However, riders are encouraged to be respectful of the natural surroundings.

3. **Headquarters Tract Trail**: The Headquarters Tract includes several unmarked small tracks where equestrian use is allowed. However, riders should make sure they are familiar with the area or carry a map to avoid getting lost.

4. **Iron Hill Trail**: This is another trail that allows horses. The forestry department confirms that the trail has a variety of terrains, making it perfect for more adventurous riders.

5. **The Ellendale Tract**: This isn't so much a single track trail but locations where horseback riding is permitted. The Ellendale Tract offers ample space and nature to explore on horseback.

6. **Holly Tract Trail**: This trail also permits horseback riding. With a beautiful landscape in hand, the Holly Tract Trail provides a charming, tranquil ride experience.

Please note that it's recommended that all horse riders practice "Leave No Trace" principles to ensure the trails remain clean and sustainable for future riders. 

In addition, please double-check local regulations before your visit as the rules and permitted activities can change.

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.