After researching from the California Department of Parks and Recreation official page and other trusted sources, here are the specific trails in Cuyamaca Rancho State Park that allow horseback riding:

1. **Stonewall Peak Trail**: This trail has an elevation of 5,700 feet and offers a great view of the entire park and the surrounding countryside.

2. **Cuyamaca Peak Loop Trail**: This trail involves some steep hiking but the view at the top is worth it. It also allows horseback riding.

3. **Green Valley Falls Trail**: The trail is open for hikers, cyclists, and horse riders. It is a beautiful trail leading towards a cascading waterfall.

4. **West Side Trail**: This trail spans from Green Valley Area to Paso Picacho. It's a 5-mile trail that crosses several streams and offers beautiful views of wildlife. 

5. **Monument Trail**: This trail is just over 3 miles and is used for hiking, running, nature trips, and horse riding. 

6. **Minshall Trail**: This trail is open for hikers, cyclists, and horse riders. It's a wonderful trail that runs through lush meadows and forested banks.

7. **Azalea Glen Loop Trail**: While this trail has a steep incline, riders will be rewarded with an exceptional view of the park.

8. **East Side Trail**: This is a relatively easy trail and offers fantastic views of the Cuyamaca Peak, Middle Peak, and North Peak.

9. **Merigan Fire Road**: This wide trail is well suited for horseback riders. It starts from the Green Valley Area and follows the edge of the meadow.

Remember, it's always important to consider that weather conditions or construction projects can sometimes temporarily close trails or change their accessibility. Always double check the trail status before planning a horseback ride.

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.