Duxford is one of a chain of communities that fill these rolling hills. Communities are well spaced to allow for plenty of forest between, so you can walk out your back door and into beautiful Arkansas forest. Walking along the roads through the forest is pleasant, or there are several rough footpaths connecting communities.
If you are tired of the forest, a relatively short hike will bring you to Lake Brittany. This is a long lake with many fingers running off through the hills. The scenery here is gorgeous, and you can enjoy some lakeside hiking or go swimming, canoeing, kayaking or boating with your dog to break up the usual walking routine.
Sidewalks are rare, and while you don't miss them along the neighborhood streets, once you get to the larger roads that connect neighborhoods you may find yourself unwilling to walk along the busy roads.
Most roads have wide grassy borders and the next neighborhood is never far, so if you just keep your dog close and cross carefully, walking along the streets around Duxford can be very nice.
A short walk through the woods will bring you to another community on Fairway Drive, which is surrounded by a lovely golf course. While dogs should not go on the golf course, walking around the perimeters when there are no players present can provide a pleasant break from the trees.
While Duxford is in the midst of many other suburbs, reducing the wilderness quality to some degree, there is still enough deep woods to support plenty of deer, raccoons, foxes, and other wildlife. You can see all sorts of migratory birdlife as the seasons change in the woods.
A short walk away, Lake Brittany offers many natural shorelines between homes, even patches of thin sandy beach on which you and your dog can soak up some sunshine. Swimming in the lake can be fun too, for you and your dog.