I've always thought the answer was no - I've always thought they cued off of other things to establish a handler's mood, like voice and body language.
Turns out? I'm wrong. A study done in 2015, which I somehow missed, demonstrated that horses can distinguish between a smile and a frown on a life-size color photograph (i.e., with no other cues as to the handler's mood). They got much more stressed when the photograph was frowning. (Of course, they used lesson horses, who are probably better than average at recognizing the mood of a stranger).
Take home: Smiling at a horse is helpful. Because they can tell you're smiling and they know what it means.