You'll often hear about "buddy sour" horses - those that pace the paddock and whinny like crazy when a beloved companion is removed for a training session, or who bolt back to the barn as fast as they can to be back with a their fellow equines. In fact, that was how I first ever learned that horses could have "friends", in human terms. In my early riding years, I merely understood it as an annoying vice that made taking certain horses on trail rides extremely challenging. But all of this behavior is due to a much bigger phenomenon called pair bonding - an essential aspect of every horse's life.
Fundamentally speaking, pair bonding for horses is like humans having best friends. You can tell which horses are bonded because they'll generally stand near each other when resting, stand head-to-tail to swish flies out of each other's faces, and mutually groom one another by scratching each other's necks and withers with their teeth. One member of the pair might even chase other horses away from their buddy.
In the above photo, Lilly and her pair bond (far right) are standing side by side in the pasture. At any point in the day, they can be seen resting together, mutually grooming or just generally in each other's vicinity. Their dynamic is fascinating to watch particularly because they are both herd leaders. Lilly is very clearly the "Boss Mare", who initiates herd movement and often stands sentry when something is alarming the horses. Her buddy is a gelding, who is very clearly "alpha" in terms of the fact that he also stands sentry in the face of "danger" (something rustling in the bushes, usually) and initiates herd movement. In fact, in the above photo, both Lilly and the gelding are watching a parade go by. They had just together initiated the herd running away from the closest point of the parade and relocating further away in the field, and stood sentry until all the noisy floats and flashing police lights faded away. Lilly's buddy is very possessive of her, to the point that he will try to get between me and her when I go out to catch her.
Of course, pair bonding occurs between all horses, of every rank within a herd. In feral herds, pair bonds often form between foals and some bonds between mares can last for years. The domesticated context changes all that, where horses often form pair bonds only to have their buddy moved to a different location or sold. Thus, horses will often form multiple pair bonds over a lifetime as other horses come and go, or simply cease forming bonds in some cases where being moved to different boarding facilities, for example, creates a constant disruption in the ability to bond with other horses. While there doesn't seem to be research into the effects that this has on horses, it's definitely a disruption of a natural social process.
That's why it's so important to not only turn horses out together in groups and give them a chance to socialize, but to group together even numbers of horses (when possible) so as to facilitate potential pair bonding. Of course, you can't guarantee that horses will automatically bond just because you put them together. Just like with humans, physical proximity doesn't guarantee friendship or that two individuals will even like each other. But it does provide more of a chance for pair bonding than putting three horses together in a field will.
It would be interesting to do a study on horses without pair bonds and compare their behavior and overall demeanor to pair-bonded horses. If you're reading this and have a horse on either side of the fence (haha), please consider contacting me as I'm interested in collecting anecdotes for a closer look at the effects that pair bonds and disruptions of pair bonds has on horses.