When we reach into a horse's physical space, no matter what, we stop its affection coming back towards us. Horses focus on one thing at a time. They are consciously either giving or receiving input, but not both simultaneously. So if the horse is trying to show us affection (which they really want to do) and we take it as an opportunity to input (touch or pet) them, we immediately stop their attempts at being affectionate towards us. This creates lop sided relationships with humans and horses where the human is always inputting the horse with what they think is affection. The horse, meanwhile, never really gets a chance to show it's affection to the human. Stand and receive the horse's affection. Keep your hands and arms down. Let them nuzzle you and gently bring their heads to you. Be still and quiet with your mind and body if you want to join with them. Empathize with the feelings you get from the horse. They live empathetic lives and look for that in their companions. Certainly you can put your arms around your horse and hug him, scratch him or reassuringly stroke him. He will get that you mean to be affectionate. But wait and do it when invited by the horse's demeanor and body language.
When a herd leader wants to allow affection from another horse, she turns sideways and seemingly ignores that horse (goes about her business of grazing). She allows the other horse to approach her and show acknowledgement and affection. It may not involve actual physical contact. But, rather feelings of acknowledgement and acceptance shared and demonstrated through body gestures, postures and mutual awareness (empathy).
I encourage humans to be more like horses and perhaps understand that less is more with horses. By that I mean we could try not to be so forward with horses. We could try to make our desires requests rather than demands. We can chose to lead like Gandhi; lovingly, firmly and quietly. We could abandon leadership like Mussolini, with his loud, controlling, fear based dictatorship. I can now understand the kind of humans who only want to be with horses. There is no self-serving ego to deal with, nor trickery or dishonesty with the horse. There is not much drama either. The horse is impeccable and that's a fact. They are honest, no matter what. They have personalities and disorders like we do but not the ego.
When your loved ones are affectionate with you know how it feels. It's the same with horses. Loving touches are noticeable and stand out more than casual physical acknowledgement like hand shakes and pats on the back. Tune in to how you feel when your horse is showing you attention. Receive the attention/affection and just say "Good Boy". There is no need for anything else. You will both understand what has occurred. You will have been mutually affectionate as giving and receiving are actually the same thing.
If you are able to establish a great amount of mutual trust with your horse, this will lead to more affection and a stronger bond. Being a great parent/leader is a wonderful way to show affection for your horse. Being the great Mom or Dad for your horse means you are there for his feelings of safety and trust first and foremost. What kinder and more wonderful way to show affection than attention to another's sense of well being. What is more affectionate than kindness? What feels more wonderfully loving than kindness? In the face of the most fearful and potentially dangerous horse, kindness is the major component in its rehabilitation (just as with an abused human). Giving your best is affection also. When your horse gives you his all and the best he's got that is his affection coming straight to you.
I guess I could sum this up by merely saying; if it feels like affection and you are not holding a carrot, it probably is. Don't try to figure the horse out too much. I think it is better to experience and empathize with how he feels. That is the real key.