Here's the reg: "Gigging means spearing or impaling fish on any pronged or barbed instrument attached to the end of any rigid object. Snagging means taking fish or other aquatic animals by a rapid drawing motion (rather than enticement by bait) using a hand-held pole and attached line with a single or one multiple fish hook. Only one single or treble hook may be attached to the line. Except, in Green River, Rolling Fork River and their tributaries, up to five single or treble hooks may be used for snagging. A rod legal for snagging must be equipped with line, guides and a reel. The rod length restriction is now removed. The statewide season for gigging and/or snagging rough fish is from February 1 through May 10. It is illegal to possess a gig on a stream or lake or in a boat from November 1 through January 31. A person may gig or snag fish from the bank of a stream during the day or night. Gigging and snagging is not legal from a platform, except that gigging is legal from a boat on lakes 500 surface acres or larger and only during daylight hours."

So, I guess you could stand on the bank and snag them, in season, even though the season was really put in place for paddlefish. But if you're in a boat on the river trying to snag anything, that's illegal.

http://fw.ky.gov/pdf/2013fishguideregs.pdf