Just as someone already said, looking at horses galloping and other references of how the legs should look like when running could help out a lot. Since the style obviously is more cartoonish than a real horse is you might have to simplify it a bit, but it shouldn't be much of a problem. Just as long as you learn how the legs of a horse moves, you can apply it to almost anything. As for the wings, the reason they look stale as they are now is because they simply point upwards as they should if it weren't flying. Try drawing them unfolded or in a different pose, look at pictures of birds when they are flying just as with the horse.
Another thing, if it were flying, shouldn't the mane flow backwards just as the tail? You have to really use everything you can in order to really create an illusion of movement, in this case you have the wind to help you with that.