I have no nice and friendly, pressure-free, purely R+ based solution for this. The reason is that with the delicious fresh grass the most rewarding thing is simply just eating it and I have
no stronger positive reinforcer. So what we are doing here is pressure-based, although it is mixed with lots of rewards.
In different parts of our walks we decide if the horses (1) are allowed to eat as much as they want, (2) eat as long as they are still moving or (3) not eat at all. When I say that "we" decide, I mean that the horses take part in that decision as well and we often choose according to their general motivation, their appetite and other things. It can change within a walk but IF we have made that decision for a given part I am very strict and consistent about it - and this is why I hardly need any visible pressure, the boundaries are rather clear here.
If we have decided that they are not supposed to eat and try it anyway, I first say or rather whisper "Na" (=no). In 80% of all situations this is enough. If they donÂ´t react there are the following steps: saying it a bit louder, making a step towards the horse, shaking the rope that lies around their neck (once), throwing the end of the rope at the horse. When he stops the chain ends at the point where he stops. And he gets a reward for not eating of course. I donÂ´t need more pressure, so there is no pain involved, itÂ´s more like a warning signal. Still itÂ´s not a nice positive way, so if anyone has better solutions I would be happy to learn.