Understanding how groups of individuals with different motives come to daily decisions about the exploitation of their environment is a key question in animal behaviour. While interindividual differences are often seen only as a threat to group cohesion, growing evidence shows that they may to some extent facilitate effective collective action. Recent studies suggest that personality differences influence how individuals are attracted to conspecifics and affect their behaviour as an initiator or a follower. However, most of the existing studies are limited to a few taxa, mainly social fish and arthropods. Horses are social herbivores that live in long-lasting groups and show identifiable personality differences between individuals. We studied a group of 38 individuals living in a 30-ha hilly pasture. Over 200 h, we sought to identify how far individual differences such as personality and affinity distribution affect the dynamic of their collective movements. First, we report that individuals distribute their relationships according to similar personality and hierarchical rank. This is the first study that demonstrates a positive assortment between unrelated individuals according to personality in a mammal species. Second, we measured individual propensity to initiate and found that bold individuals initiated more often than shy individuals. However, their success in terms of number of followers and joining duration did not depend on their individual characteristics. Moreover, joining process is influenced by social network, with preferred partners following each other and bolder individuals being located more often at the front of the movement. Our results illustrate the importance of taking into account interindividual behavioural differences in studies of social behaviours.