My brother and I had an excellent trip at Cuivre River. Using the Equestrian Trailhead, we hiked a combination of the Cuivre River, Big Sugar Creek, and the Hamilton Hollow trails to make a nice 8 mile, overnight loop. We stayed at the backcountry camp at junction no. 20 where we could make a camp fire. It made the 30 degree night extremely pleasant.
The Cuivre River Trail on the west side of the park is really a gravel road suitable for car traffic. Many of the other trails in the southern half of the park are made for equestrian use. Even if they aren't, horses go there anyway. This has its good point -- it made following the trails, which were very obscured by all of the fallen leaves, easier to follow. Many of the trails I followed could be better blazed for easier traveling. But my GPS and compass, with the great map you get at the visitor's center, made the trails fairly easy to follow.
I heard a yowling at about 5:00 to 5:30 in the morning that came from what I think was a bobcat. It was a sound that seemed other-worldly and unnerving. And it was relatively close. We saw lots of deer, including a few bucks that didn't seem to be that frightened of us. Hunting, I'm told, is not permitted in Missouri State Parks.
The backcountry camp was great! Don't forget your compass and a map, or you might be spending more time in the park than you intend.