Depending on the date you are coming, there is an airbnb located about 1 mile down the road. https://www.airbnb.com/rooms/26685022?location=Fayetteville%2C%20AR%2C%20United%20States&search_id=68122b70-40eb-4420-82ba-1f0e0d69b38f&federated_search_id=191d74b4-c9ae-494c-b536-d0c06a6ceb00
Mount Sequoyah is a retreat and conference center in Fayetteville that has hotel style rooms and a few houses. It is about a 15 minute drive from the winery.
Sleep Inn or La Quinta Inn & Suites off Millsap Road in Fayetteville AR would be the closest. Both 4.7 miles from venue.
Not sure it's out in the country. We stayed in Bentonville, but that was a good 20 minute drive.
Thanks! Your answer is awaiting moderation.