That is not an easy position to draw a horse in. (dangling preposition)
Usually we draw horses standing and it's more natural to have a feel for the porportions. But here, you can't go by what's familiar. You have to really LOOK at the photo and draw exactly what you see, so that the forshortening and all come out. And your have done this with remarkable accuracy! The lines of the back, and the way the back feet tuck up under the tummer, ALL just exactly like the photo!!!
The only area that is just a wee bit , shall I say, stiff, is the face. In the photo the mane covers a bit more of the face, giving it a bit more of a cute, peeking feeling, and it isn't stick straight. Helps to give hair lines a bit of a "wave" to them to help the viewer read them as "hair". They drape over the bone structure of the face, though in this case, dead straight on, not as evident .
The other tips on cross hatching are good. YOu can use this to help describe round surfaces, like the leg itself. It is basically long , roundish shape, like a cylander, so cross hatching or shading lines that help define that roundness help.
Yes, the idea to "ground" the horse with some background is good. Look at the shadow around it, maybe some dark lines, in a parallet to the ground motion , will say "ground" and "shadow".
It's a charming piece and quite recognizeable as THAT horse.