Nope. Horses just don't react like that. They certainly can show affection, and form attachments, but they are very much creatures of the moment. They certainly remember things, like the reaction my mare had the day I brought her home, after she had been away from the property for four years, but they don't think "Oh, I don't see So-and-so anymore, I will be so sad."
Y'know, my horses nicker when they see my car coming (usually because it's feeding time) and they usually get pretty excited to see me. But then again, I've had other people feed them, my dad had to do it for all the months I was in the wheelchair recovering, and they nicker when they see people coming (even total strangers) ... the ungrateful monsters (kidding on that last part). It's just part of being creatures of habit, living in the moment.