In the animal kingdom, there are many things that can influence behavior but generally we look at emotions as being the primary driver (stimulus) for behavior while reinforcement or punishment determines whether that behavior will be repeated in the future.
Stimulus - Emotions: Jaak Panksepp’s book Affective Neuroscience has one of the most widely known categorizations of human and animal primal emotions. As an expert in neuroscience, Jaak studied the brain, performed laboratory experiments and categorized basic emotions (brain systems) as follows: RAGE, FEAR, LUST, CARE, PANIC (Grief), SEEKING and PLAY.
The names were capitalized by Dr. Panksepp to highlight them as identified brain systems, as opposed to their use in the vernacular.
This system of emotions, how the individual reacts to them, and whether their reaction is rewarding or punishing, results in the creation of a resource access hierarchy between individuals. So, what we call dominance, is just a connection between emotions driving behaviors and behaviors being rewarded (success) or punished (unsuccessful).
Furthermore, researchers have also noted that just because an individual gains access to a resource first, does not mean they won’t follow another horse’s lead or choices in other situations. Nor does it mean that an individual with first access is the “alpha” of the entire group, in every situation.   Resource access and leadership can vary between individuals, groups and species. This can also be impacted by individual and environmental factors such as captivity, health, age and so on. Therefore, in horses a resource hierarchy is established to quickly avoid conflict and establish social norms, rather than determine who is “boss” or “leader” of the group. (The referenced study in this paragraph noted that in feral horses, mares of all ranks within a hierarchy could initiate group movement and be followed by the rest of the herd).
One other interesting set of behaviors related to emotions is the appearance of calming signals. Calming signals are often considered “submissive” behaviors from those lower than the alpha, when in fact they are just communicating conflict avoidance or the release of tension. They don’t indicate that an animal is “submitting” to one of higher rank in the sense of dominance. Rather they are attempting to prevent aggression and possible injury in that moment. Other herd members have even been noted to use calming signals to prevent aggression between two other individuals. 
Lastly, we should all be aware that during training, the techniques we use have an impact on these emotional brain systems. Ja