Hi Bart, The head doesn't add anything to the composition. The picture isn't about a horse's head.
I know Russ, but since I do not know what was cut-off (it might have been a headless horse to begin with), I do not know if it would change the impact, any/much. That's all.
Maybe it dates back to my early days when I was taking my exams for the license of Professional Photographer, and I submitted one assignment with (delibrately) cut-off objects / props, except for the one main subject. It was hard to convince the examiner's committee ... (although in that case it was clear what was cut off).
Cheers,
Bart