bassets,
I just got back from the Fort and went to the HDDR a week ago (Saturday 3/22). After it was over we walked out past the Wagon Ride loading area and the wagon/horses were still there but they had many people in the wagon already. I have pix of this in a trip report
http://www.disboards.com/showthread.php?t=3252856
The pix of the HDDR are in post #14 and pix of the horses/wagon in post #15. So I would think you could do it but don't dilly dally in between.
Bama Ed