Stone island is a short half mile walk and an even shorter water taxi ride for $2.00 per person round trip. Just turn left as you leave the ship terminal. Walk on the sidewalk less than a half mile until you see the little "Embarcadero" sign and ticket booth. The little taxi pier is right there too. Thus itt is very easy to get to Stone Island on your own. The taxi boats run pretty much on demand
Carmelita's is an excellent clean and tasty outdoor restaurant with amazing service. They cater to your every beachy need while you are there.There are lots of activities available there on the island.
You should probably contact that vendor to answer your horse question.