I'll tell you my own experience with doing the above.... and why I would never do it again.
My puppy was doing well on the ground with commands, but like you I wasn't sure if she was ready to listen when I was up on a horse and wanted to be 100% sure. I tested to rope with and all around my horse, I practiced tossing the rope over his head/rump if the puppy decided to change sides and he wasn't fazed at all.
We went on the trail ride and it went great... The puppy was staying with us, the horse was tolerating the rope and I kept it tight enough the puppy couldn't get herself too mixed up without hitting his feet.
When we got back to the barn however... we were walking the long road to the barn when two barn dogs came running up to play with my puppy. My dog was a little timid around other dogs and two full grown dogs running scared her, so she ran away and they chased. It happened before I could drop the lead rope, but she wrapped herself around all four legs of my horse so tight she was RIGHT next to all of his hooves. The poor horse had all his legs tied together and wasn't even acting worried, but because of the rope pulling he took one step and she was so close to his hooves he landed on her paw.
It was the worst moment ever, she cried SO loudly I thought her leg was broken! (I still give props to that horse, who even being tied up, having me hop off and abandon him for the screaming puppy while two dogs ran amok he just sat and watched) Luckily since she was a puppy her bones were 'flexible' and the vet said she only had a fracture at most, but it was still a terrifying experience for all involved (my puppy took the pain and related it to the dogs, not the horse and was very skittish around dogs for a while after that)
If I were to do it again... I wouldn't. I ended up buying a vibrating e-collar that I trained her with on the ground, and then transferred to the horse so she wouldn't learn to 'get away' with things when I was unable to actually get her.
Take a ride across the badlands
Feel that freedom on your face - Breathe in all that open space
You'll understand why God made -Those fly over states