This is a ride on the horse trails. There are not designated bicycle trails at the park. But you can ride on any trails that are horse designated trails.
You are required to yield to horses. Pull off the trail, and let the horses pass. Then continue on your way. If you come up on a horse, you are required to wait until the horse rider allows you to pass.
You need a Discover Pass to enter the park. You can buy one at the gate. Enter on Burt Road, park in the main parking lot, and then look for the horse trailhead by the entry gate. Pick that up, and then just ride the perimeter of the park. This is the main trail, there are several other spurs you can pick up along the way as well.