Yatesville Lake State Park Campground is a 1.7 mile lightly trafficked out and back trail located near Adams, KY that features a lake and is good for all skill levels. The trail is primarily used for hiking and camping and is accessible year-round.
There is another trail system there called the Mary Ingles trail that is about 3.5 miles long. I wasn't too thrilled with the trail. There were parts with really tall grass, and wasn't all that scenic, besides one awesome view of the lake, and a frog pond towards the end.
There is a trail near the marina at Yatesville lake. Well maintained, nice views of the lake and great with kids.