Our family had a terrible experience horseback riding with Bayside. My daughter (11) was thrown from her horse when hers and 2 others bolted. My son (7) also fell off. The third child (from another family) managed to hang on until she arrived back at the stables. My son fell on the road, far out of my sight and suffered severe road rash. My daughter broke both bones in her left arm very badly. In preparation for our ride, the kids both took horseback riding lessons at home, but were definitely beginners.
Long story short. We had to fly home half-way through our vacation. It was an extremely frightening experience for us all.
We will not ever go horseback riding outside North America again. Others on this board with vast experience have subsequently warned readers about how inherently dangerous horseback riding is and on top of it there seems to be problems with this stable in particular, and I was not confident in the medical facilities. Kind of a bad mix with lots of potential to end up even worse than it did for us. I think there is a good reason Disney does not offer this as an excursion.
I'm pretty sure you can do a search on horseback riding and find the threads and decide for yourself.
Whatever you do decide, I hope you have a wonderful, safe cruise.