Nope, didn't need any horse items crossing the river. The stamina stimulants were mainly for speeding up the journey on the cheat horse. So, at 3:20 you can drop off the edge, die and respawn in Guarma, but you can't use any cheats there. So option 2 is if you want to ride around instead of walk everywhere once there.
Strangely though, you can whistle your horse in RDO whilst in Guarma, just not in story mode.