Nope...we don't hunt ducks here in Arkansas. What are ducks?
Listen to what Jim said. Extracurricular activities are going to be "slim" and "none", unless your cabin/lodge has satellite tv, pool table, etc.
DeWitt is the closest town of any size, but that isn't saying much. Stuttgart is the next town, with Mack's Prairie Wings, RNT, Grand Prairie museum, Wal-Mart, restaurants, etc. Little Rock is (if I remember) in the 2 to 2.5 hour range away.
What days are you coming down? Might be able to hook up and have a bite to eat in Stuttgart...about 40 miles east of my house...especially on a weekend.
One thing I would consider bringing is a camera, and doing some driving around - some of the rice fields between DeWitt and Stuttgart can offer the chance for good pictures, depending on weather, etc. Just get a State map and you can't get too terribly lost, especially if you stick to pavement.