Dogs with Horner's can lose muscle tension in the face-- Simon's eyeball would sort of fall back into the socket, which made him look a little scary-- and he required artificial tears on occasion. From what I understand, though, some dogs will go slack and look like they've had a stroke (as Simon did), then after a while, the reverse happens and you see what Suzanne mentioned-- the tightening of the muscles. They sort of swing one way or the other or both.
But the bottom line is that it's a neurological condition where they lose muscular control in the face. The good news is that it's not painful for them (at least that's what I was told, and Simon never seemed bothered). I just had to warn visitors that he was not a zombie dog.
"In these bodies, we will live; in these bodies we will die.
Where you invest your love, you invest your life." --Marcus Mumford