Horses are majestic creatures. Their powerful size alone demands your respect. Its not easy getting a close up shot.
What I've discovered is if the goal is to capture horse portraits or head shots the trick is to get the proper shot angle.
Horses have large odd shaped heads and they stand significantly taller than most humans. Most of the time a photographer ends up shooting up or at the same level as the animal. Sometimes this will distort the horse's muzzle or give unflattering results.
When photographing head shots and portraits its important to get close and fill the frame. Profile shots work really well.
My strongest recommendation is to squat down get low and shoot up
at the horse. This produces some very dramatic shots with the sky in the background. Be sure and meter for the sky and use a fill flash on the horse. I think you will be pleasantly surprised with the shots you take from this unique perspective.