The Altus Wine Trail is about 4.3 miles one-way and would be a somewhat hilly bike ride. If Altus or the wineries got serious about promoting this trail, it looks like you could make it a more scenic walk/mountain bike by connecting Chateau Aux Arc to the dirt road just to the west that loops down to Wiederkehr (see map below). From there it is just about a mile and a half to Post and nearby Mount Bethel. You might even be able to find an alternate route down the hill to avoid 186, but I have no idea what the property boundaries look like there.
I'm not a wine expert, so if you have strong feelings about any of the wineries below let me know in the comments!
Chateau Aux Arc - This is one of the newer wineries and in my opinion it has the best landscaping and
nicest grounds. If you are a fan of having picnics at wineries, this would be my choice. I've only been twice and the first time they didn't have many wines to choose from, saying the grapes struggled the previous year. On our more recent visit, they had a good selection and I liked the fact that most of their wines use grapes grown on site and I believe all their wines use grapes grown in Arkansas. They also do a lot with American/native grapes and have strong sustainability goals. Their Dragonfly Red was my favorite.
Wiederkehr - Opened in 1880, Wiederkehr basically pioneered the wine industry in Arkansas. The distinct architecture makes this a great place to visit and there is a restaurant on site. I like their muscadine red wine (classy right?) and am a sucker for native grapes. My only complaint about this place is that parts of it are in need of updating or renovation.
Post Winery - Post Winery has a nice tasting room and their tour is interesting since St. John boxed wine is produced here as well. I am not a white wine person, so I could be way off on this, but I think they have the best selection of white wines along the Altus Wine Trail.
Mt. Bethel - I think I've been, but I don't remember anything useful. I'll be sure to add more after I visit again. I think they have a wide selection of fruit wines.
For a complete list of wineries in the state, visit http://arkansasgrown.org/ or http://www.arkansas.com/
View Altus Wine Trail in a larger map