There is always a lot of discussion that regularly does the rounds on social media surrounding the question, is Positive Reinforcement “good” and Negative Reinforcement “bad”? First of all, I would ask, for who? The trainer or the horse/animal?
You are then assured that positive simply means adding and negative simply means removing, that’s all, phew! But that’s not the full story, that’s only half the facts. If you see someone suggesting that Negative Reinforcement is ok or fine or benign, because it’s not bad, it’s just removing something, RED FLAG! 
I’ve said this many times in the past, always question and verify information and not take things at face value on social media. We are all learning and at different points in our learning journey and that includes me, so this is not a criticism. This is me trying to help people understand and disseminate information about training and behaviour change. We can all have opinions, but there are also facts and sometimes the absence of certain facts, can change the very nature of the message.
There’s an important difference between Negative and Positive Reinforcement, ie. one involves an aversive (unpleasant) stimulus and one involves an appetitive (pleasant) stimulus. Think about that for a moment, one stimulus feels uncomfortable enough for the horse, physically, mentally or emotionally, to elicit some kind of behaviour change, that we can then reinforce by the removal of it. We might like to think about it as “mild pressure” but it was still strong enough to get some kind of response from the horse to attempt to escape or avoid it. Negative Reinforcement is also called Escape and Avoidance Learning! If it were that “mild and gentle” it would be neutral and the horse wouldn’t change their behaviour in order to escape it.
I also need to emphasise that there is more than the “4 quadrants” involved in learning. This is important to know, because we need to consider not only how horses learn, but also what is being paired (associated) AND how they feel while they are learning.
There is Operant Conditioning and there is also Classical (Pavlovian) Conditioning and there are also other ways we learn. Classical Conditioning means that along with the stimulus there is a response, there is an association being made and that can be a feeling, an unpleasant, a neutral or a pleasant feeling or any feeling in between. Via Pavlovian learning, we become associated with these feelings. If you train mainly with Positive Reinforcement, you’ll have a horse who mainly likes you and the training, except in certain contexts. The exception will be in the contexts where you use Negative Reinforcement. If done well and enough of it is done, the Positive Reinforcement can bleed into other interactions, if you are lucky. Horses can be very specific about aversives because they can be very specific about context, they have excellent memories and they have scales in their brain weighing everything up.
We can get a seemingly calm and willing horse, because control may be a primary reinforcer, whether that’s control of the addition of an appetitive or understanding what to do to remove an aversive stimulus. It doesn’t mean they’re having fun, it simply means they understand how to avoid the aversive stimulus. But remember that they had to first feel the discomfort of the aversive stimulus and they also then made the connection with who applied it in the first place, YOU, before they figured out how to remove it. A negative emotional valence does have an impact and can impede learning processes. A perceived threat can disconnect horses from learning (and the trainer) and negative emotions can also lead to low motivation. Makes sense right?!
To sum up, an easy way to remember all this is that we have Skinner (Operant Conditioning) on one shoulder and Pavlov (Classical Conditioning) on the other when we are training.