It may sound crazy but being from the area I've never stayed at a cabin around the lake but I do know there are plenty around. BarrenRiverblog | Enjoy all that the Barren River, Barren River Lake and their communities have to offer.
The site will show plenty of cabins and also lake conditions and levels. It also has maps worthy of looking at. I'd also recommend Barren River Lake State Lodge. They have cabins and also the main lodge that houses a buffet that I have enjoyed many times.
Barren River Lake State Resort Park - Kentucky State Parks
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Everything is possible. The impossible just takes longer!