Is it because the aqueduct wouldn't take the extra weight? Unlikely.
Would the horse's hooves damage the nice flat surface? Possibly, but I don't think that's the reason either.
No, I think it's because the far (south east) end is stanked off, reducing the canal to a weedy ditch.
This is the Cromford Canal's
I talked about horse drawn trip boats recently, but missed this one. Apparently the Horseboating Society tows narrowboat Duchess on demonstration trips (no passengers) between Cromford Wharf and the aqueduct on heritage days, presumably coinciding with steaming of the Leawood Pumping Engine. In the 1980s the then Cromford Canal Society ran passenger horse drawn trips, but these didn't last.
Back to the top photo: the sign actually appears to prohibit horses from leaping over the wall. But, assuming it refers to the towpath, if you were leading a horse from either direction you wouldn't know where the prohibited zone was.