I think you have a good start.
Personally, I think you should play around with the lighting a bit as the background and horse lighting does not match.

I'm seconding everything Emerald said. Also, the lines on the horse's shadow are very sharp, when in that lighting they'd be rather soft. I would recommend blurring the background a bit, too; it's very busy and draws attention away from the horse.

Pretty much what Emerald said. Go around with the eraser tool one more time since I saw some green stuff (grass) around the hair. And maybe change the eye color and/or make it brighter. Outlining would be great. The hair needs some softening and less smudging. And maybe make the shadow a bit more faint as it’s on snow, so it should be a bit more faint! :)

You have a really good start. In addition with what has been said I think if you can try blurring the background a little it may help the horse pop. You could also experiment with lighting to bring attention to certain areas.