Ok - this thread had me intrigued so I have done some (very low key and anecdotal) testing today.
To make horsie lead nicely, with her shoulder at mine, if she is distracted, I stopped, called her name and went off in a different direction. Took her about 2 minutes to clue on to that. (Same way I trained my dogs to walk on loose lead - whether singly, in pairs or in a group of up to 4.) I did “stand, wait, come” games - with the dogs, this is “Sit, wait, come”). Yes, I only went to the end of the rope with horsie, but, again, very few repeats and she got it. Wont take long to get that into an “off-lead” stand :D. I teach my dogs a trick where they pick up one foot when I point to it - good for the vet or yourself when examining and necessary training for agility - they need to know where their feet are. Started training horsie to pick up one by using a target stick - same one that I use for the dogs (well, it is an old whip - it was handy). About 50% there - horsie is finding it a little complex.
My horses come when I call “COME”. They back when I say “BACK”. Heck, they hang over the fence watching when I am training the dogs :)- I am sure I could teach horsie to retrieve if I could find a big enough dumb-bell :D.
I don’t treat my horses like dogs, but I sure train them the same - hand signals, voice commands and all.