Horsea-- you and you horse both look happy!
I did try that a couple of times, the training programme I was in a used that for one of the lessons, but a couple of people said the rope had got caught, or their horse had stood on it? , I can't remembet the exact details but the outcome was a couple of horses with cut mouths and that put me off trying it again.
I have to say it wasn't a thick rope like the one in your picture, it was a thin savvy string. I don't think the thicker rope would cause a cut.