“They can just walk away if they want to.”
Who has heard this statement? I have, many times and it always gives me pause.
I find with equines, that they don’t usually leave to enjoy their alternative food, which I always recommend having nearby when training. There’s a funny saying we use for clicker trained horses, we call them “velcro horses” and there’s lots of reasons for this!
Often if they’ve had any kind of traditional/aversive training or handling, they can be afraid to leave. A horse or pony or donkey walking away from a human would be prevented or punished for a variety of reasons. Swinging their butt to a human as they depart is often labelled “disrespect” and a threat to the human. Or it could simply be a matter of Negative Punishment, they don’t want to leave the immediate and closest food that is on offer. They need to learn they have choices and can look for reinforcers elsewhere, it’s often something they don’t know and it has been drummed into them that they must never walk away from a human.
They may not want to leave if they’ve commenced Positive Reinforcement training and the first thing we do is some basic static training such as teaching “manners” around food. This means we are highly reinforcing the horse’s behaviour of staying with us. Also, when we start each session, we often start with some simple behaviours and all of these are usually with the horse right beside us. Standing next to us becomes the “hot” behaviour, ie. the most recently reinforced behaviour is what the horse is most likely going to offer us.
They also stay because often what we are offering is higher value than their boring hay in a net that they get every day.
There’s also the possibility of contrafreeloading making the food we are offering more valuable, even if we think it is of equal value to the alternative food nearby.
I find that horses stay, but give a lot of hints with their behaviour (latency) and/or body language that signals their displeasure, rather than just walking away. You might see pinned ears, tense face/lips, flared nostrils, whites of the eyes, they might circle you, push on you, take the food roughly from your hand or do a double bite down when they take the food from your hand or the bucket. There are many behaviours and indications of their discomfort that they are shouting at us. In my experience, only super fearful equines tend to walk away and that’s usually if we’ve tipped into R- and they’re trying to remove the aversive stimulus, which could possibly be us!
I find that more experienced R+ trained equines can learn it’s ok to leave, but it is a learnt skill. It’s not really something I want to see the horse resorting to when I’m training, it means I’ve made a pretty big boo boo 
If I’m teaching people in person and my horse leaves the student and comes to me, it’s a good sign that the criteria is too high and/or RoR is too low, so my horse goes elsewhere to find reinforcement. I love that about them, it’s a pretty clear message with their behaviour. But it is something they need to learn and feel safe to do.
At the end of the day, Positive Reinforcement training should be fun. If we set the bar so low as to think that if we train poorly or muck up, the horse will just walk away, then we really need to train better. If the horse we are training tells us in their behaviour and body language that the training is not fun, it’s best we listen and endeavour to be better trainers.