Most horses will socialize well with humans, but only if the human responds to their cues. This is unlike dogs, who will initiate more interactions.

Eye contact is meaningful to horses. If a horse looks at you, they may be asking you to look back. If you do, and they continue to look at you, you've made the first step to connection. The ears will usually go forward at this point. That gives you permission to approach. If you then offer an open palm, you'll probably get a muzzle touching your palm. Now you've been accepted as being allowed to touch the horse. This little hello social ritual works with most horses, even ones who don't know you.

When you see someone approach a horse that knows them, they'll usually do this without thinking about it. You'll see the eye contact, the ear movement, and the muzzle touch, in that order. Horses have strong flight and startle responses, and this defuses those.

Read "Talking with Horses", by Henry Blake.[1]

So few people get this today that Horse Guards in London no longer lets tourists get near the horses. For over a century, they did, but the cluelessness level got out of hand, and about two years ago a white keep-out box was painted on the pavement. This is partly a cell phone problem. People would back up to the horse to position themself for a picture with the horse, without ever making eye contact. Horses read a backwards approach as an unexpected approach and possible kick threat. Some tourists got nipped.[2] The usual "No" sequence from a horse is ears back, bite threat, nip, serious bite or spin and kick. If you approach backwards, you don't see the horse saying no.

(You can discuss a "no" with a horse. I had to do this recently when I was getting my horse out of a new pasture. The boss mare, who's a good herd leader and protective of her herd, cut off my horse to keep her away from me. So I had to talk to the boss.

I walked up to her and stopped about a horse length away, outside threat distance. Made eye contact. Didn't get an invitation to approach. So, hands at sides, I took a step forward and motioned with my hands for her to back. She backed up a half step. That was a mild submission. Now I could catch up my own horse without her interfering. My own horse came to me when called, while the boss mare watched carefully. I haltered my own horse and took her out, with the permission of the boss mare.

This is not disobedience. This is a competent alpha mare doing her job. She watches over the herd, chases coyotes and wild turkeys away so the other horses don't spook, collects up the herd under a tree in bad weather, and somehow seems to settle disputes. The horses don't get injured.)

[1] https://archive.org/details/talkingwithhorse0000blak_r2k0

[2] https://www.youtube.com/watch?v=Up5_haF98z8

How we manage and engage with our horses shapes their personality