I'm not sure that the fence "spoils the shot"... the gate's not so photogenic, but it's part of the scene. Of course you could have created a super clean shot of just the horse's head or perhaps moved the camera just a little bit lower and gotten rid of the gate, but I do like the rail fence. One of the big secrets of Photography is making absolutely sure that everything you want is in the frame and nothing that you do not want is in the frame.
Famous photography teacher David Vestal used to tell people that they're your pictures, so make sure that everything you want is in the frame, and nothing you do not want is included. I learned this advice over 40 years ago and it is good advice. I think that learning photography today with a much larger viewfinder image on a phone is actually of some benefit. When I was learning photography I had a rangefinder type camera with a teeny tiny viewfinder image. A single-lens reflex has a bigger image, and the phone has an image that is as big as 3 inches or more tall, and I think this is actually an advantage over a traditional camera.
I actually like the use of the out-of-focus fir tree in the background of the shot.