Yes, you will capture a few shots that look fine without your intervention, but as someone who works with both digital photography and analog film photography (including processing and printing my own negatives), the editing process is an integral part in bringing out your voice in most of the photographs you'll take - that goes for anything, not just model horses. Taking a photograph is a collaboration between the camera and the photographer, not just one or the other.
If I'm hiring (and in turn paying a decent sum of money to) a professional photographer to shoot something, they better make those photographs look as great as they possibly can. More often than not, this will require some amount of editing.
Now, I'm sure when most people think "editing," they picture your typical Instagram-style photo: washed-out colors, hipster filter, maybe some words or overlaying textures. That's another topic for another day and doesn't really belong in this discussion. Still, people tend to unfairly group post-processing in with this. I have seen so many fantastic photos that would improve tenfold with just a little zap of vibrance or contrast to make them full of life!
I will unashamedly admit it outright: every model horse photo on my deviantART account has been edited in some way - usually with just what I call "darkroom edits" - i.e. techniques that would be found in your typical darkroom setting such as adjusting contrast, burning, and dodging, and sometimes I may add a pang of vibrance to make colors pop a bit or adjust the tint (especially with snow photos, which often turn out very blue) to balance the colors if need be. I often shoot in RAW format, so my go-to editing software is Adobe Camera Raw, which is used by both amateur and professional photographers.
Take the photo below for example. The top one is "no edit" and has not been touched since being imported from the camera. The bottom one has gone through simple post-processing in Camera Raw.
All in all, what I'm trying to say here is that editing is an awesome way to give your photos a little bit of an edge within the vast sea of other model horse photos. It's not wrong, it's not cheating. You don't need any expensive programs to do it, either - there is a ton of freeware across the internet for photo editing that can do subtle changes along with bigger ones. Be creative and have fun.