*waves* As someone who is OBSESSED with photos of her animals I totally want to encourage you to pursue that
Really really cute horses! I'm not a professional photographer but I am often bribing people to come take professional photos of my horses so I can give you some "advice" as a would-be client!
I would try to take photos free of 'distractions' to really show off the animal. By distractions I mean any fences or wires in front of the horse. Imagine the 2nd photo from the top if there was not a fence in the way and at a slightly different "more centered" angle.
Usually my favorites are expressive with alert ears and eyes or that capture the animal doing something characteristic and charming.
When taking my own pictures of horses I find it sometimes helps to lower the camera to be "level" with them or try creative angles.
You also might try investing in a fancy high resolution camera where you can play with the focus and really get creative.
I hope some of that made sense, if not feel free to ignore me XD