Haunted Hay ride.
Have two really good actors sitting on the wagon talking about the terrible accident last year and how the hay rack rolled into a gulley and several people were really messed up.
Paint canvas or other material with flat black paint and display it next to the trail with warning signs coming up to it about "Dangerous Drop Off", then have some small , shallow holes right there for the wagon wheels to dip into to make it seems as if the whole wagon is tipping over.
I recommend experiementing with the depth of those wagon-rocking holes , you don't want them too deep to actually roll the wagon over, you know.
Installing some pipe railings on the wagon would pretty much be a "Must".
You do have to anticipate what could happen in all situations.
If you had more than one trail or path for your wagons then you could bill the one as the "Dangerous" ride and maybe even only allow more able-bodied people on that wagon, versus Mothers holding small children.
(Disclaimer: I have never operated a hay ride myself, I just have alot of ideas.