I agree with the previous posters. You definitely have a good eye, now you gotta train it! :)
I'd work on watching lines in your pictures. Like in that third picture, the reins being held off frame draw the eye down and away from the subject - the horse! You want the eye to stay on your subject and not get drawn away.
The first one, those trees appear to cut off the horse's line of sight (logically we know they don't but the eye thinks they do) which makes the photo a little awkward to look at.
There's also a matter of movement. When an animal, or human, is gazing out of the picture, you want to give them gazing "room". The first photo is really great that way, you feel like you can see where the horse is looking. The 4th, 6th, and 8th all could use help that way.
And then there are little things like cutting feet/hooves off here and there. You want to watch that. I like to crop the picture smaller when I make that "mistake" and maybe crop it enough so that something else is a little chopped off. So if a foot is gone, I might crop is so the ear tips are cropped out too. It makes your "mistake" look intentional.
Final thing, I LOVE that one with the girl and dog "dancing". Though they're close to the edge, the dog is "keeping" the girl in frame and since they are so far over, it fascinates the eye. That tuft of grass in the background draws the eye to the subjects - girl+dog - and there's nothing to draw your eye away so you stay stuck on the subjects which is exactly what you want to have happen. And the movement in the girl's skirt... I just love it!
Keep taking tons of pictures (I had a teacher tell me once that, if I wanted to be really good, I should take 100 pictures per day, everyday, to really work my "eye") and , if you can, like Jake and Dai said, try to take some photography classes. I think you'll love taking them and you'll learn so much about the art of photography. :)