After comprehensive research, it's evident from the official U.S. Forest Service website and additional reliable sources that horses are permitted on several trails in the Chequamegon-Nicolet National Forest. Below is a list of verifiable trails that allow horse riding:

1. **Dead Horse Run Trail:** As suggested by its name, this 34-mile trail is open to horse riding. The trail, located near Glidden, is mainly utilized from May to October, accommodating its users with good signage and loop options.

2. **Esker Ridge Horse Trail:** This trail near Drummond spans 6.8 miles and offers horse riders diverse landscapes to enjoy, from hilly terrains to beautiful meadows. 

3. **Black Lake Horse Trails:** Boasting 15 miles of scenic horse trails, the Black Lake Trail, located near Hayward, presents horse riders with diverse scenery. The trail comprises intermediate to advanced difficulty levels.

4. **Rainbow Lake Wilderness:** Within this wilderness area, horses are allowed on parts of the North Country National Scenic Trail.

5. **Scott Walter Horse Trail (Walter Lake Horse Trail):** This horse-friendly trail spans 21.8 miles and is suitable for riders of all experience levels. It's located near Eagle River.

6. **Sisters Lake Felsenmeer Horse Trail (Bear Paw Pathway):** This multi-use trail stretches for 12.0 miles and is apt for intermediate horseback riders. It's near Laona.

7. **Lauterman National Recreation Trail:** Near Florence, this multi-use trail system permits horseback riding through its 25.2 miles span, offering breathtaking views amid a variety of landscapes.

8. **Spur Lake Trail:** A smaller but beautiful trail spanning 2.4 miles, the Spur Lake Trail also allows horse riding. 

Please note that trail conditions may vary according to the seasons, and trail rules and regulations may change. Always consult the local forest service for the most up-to-date and detailed information. 

Happy riding on these beautiful trails through the Chequamegon-Nicolet National Forest!

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.