According to the official Connecticut Department of Energy and Environmental Protection (DEEP), Pachaug State Forest in Voluntown, CT provides hiking trails accessible to equestrians. After careful research, the following trails allow horses:

1. Mount Misery Trail: This trail runs through Pachaug State Forest and is open to horses. It also offers beautiful landscape views to enjoy while horseback riding.

2. The Narragansett Trail: This trail cuts across sections of Pachaug State Forest and allows for horse riding. It is a part of the larger Connecticut Blue-Blazed Trails system.

3. Nehantic Trail: Another trail that allows horses, featuring several water bodies along its path. 

4. Pachaug Trail: This is a 30-mile loop trail suitable for horse riding. It features beautiful wildflowers and is accessible for use all-year-round. 

5. The Quinebaug Trail: Listed by the Connecticut DEEP as a horse-accessible trail that meanders through beautiful greenery in the Pachaug State Forest.

Remember, it is always recommended to check the updated information before planning a visit and to follow the "Leave No Trace" policy to maintain the beauty and cleanliness of these trails.

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.