NW Arkansas is NOT known for its duck hunting. Most of the quality duck hunting is in NE, E, and SE Arkansas. There are a few lakes up that way, but I've never heard of anyone hunting them. If you are looking for good duck hunting, head to the prairie on the NE side around Jonesboro or on the East side toward Stuttgart, Searcy, Des Arc, or south down toward Overflow and Felsenthal NWR. Outside the prairies, you will need a boat, as most of Arkansas's best hunting is in the green timber.
There is plenty of public duck hunting in Arkansas. There are the rivers and lakes of East Arkansas and a couple of NWR in South Arkansas. Bayou Meto is a big public area but its very, very crowded. White and Cache Rivers are good as well. Just get on the Arkansas Game and Fish website...lots of good info there.