I'm sorry for the people who own or lease a horse but don't keep them at home. I know this is getting more difficult to do as property is at a premium and not everyone lives with enough room for a horse. You develop a special relationship with anyone you live with and horses are not an exception to that rule.
I've had quite a few horses in my life. I got my first horse when I was eleven. For 2 years of college, I was horseless. Then I had a stable where I taught and kept my horse there. After that I almost consistently had horses at home, including when I moved from the East Coast to the West, then to Kansas, then back home. The horses went with me.
Now I live with Ziggy, a TB/Oldenburg mare.
It's true she doesn't technically get underfoot the way the dogs do, I'm more under her feet, but she's naturally curious and wants to be with me. Unless there's delicious hay and then I definitely am less interesting than that.
While horses are herd animals and they really enjoy being with their own kind, they've been domesticated and do bond with humans, like dogs. The more time, not working, not training, not rushing to get done, you can invest in your relationship with your horse, the happier you will both be. If you can't keep the horse at home, set aside time to simply be together. You will be rewarded.