I have to agree mostly with CC on the photos, but I just wanted to give what I saw. I will go in the order of the way the links are posted.
1st photo – Not sure if it the DOF or if you masked out the background but the outer edges of the horse are too soft. I don’t know horses, but having the mane draped over may have looked better, but then again, I don’t know the horse or your situation. What was the background? A key light behind the horse may have gave the image some more depth. Just guessing here since I’m not sure what was there and what you had to work with.
2nd photo – Horses in motion can be very dramatic shots. The muscle tones look good but IMO could use a bit more contrast and a different angle. Truly, no one wants to see a horse’s ass. In this case a fill flash would have made the image worse by highlighting something that should not be highlighted. These shots can be trying to get, sometimes you got to spray and pray because going in the corral may not be allowed and be dangerous. If you were at the 2 – 4 o’clock position taking this shot, things would have been greatly different.
3rd photo – Agree with CC, fill flash on the right side of the horses face would make this better. I would also crop out that distracting string in the upper right-hand corner. As small as it is, it draws my attention away from the cute little pony. I “assume” the uploaded image is a low-res version? I zoom into it and it looks soft, rightfully so if it is a low-res version. If not, it could use a slight bit of sharpening, but not too much. Otherwise that shot is something I would see in a cutesy calendar.
4th photo – fill flash or reflector to see the horse’s face details. The lens flare looks good but the horse’s face is way too dark, too dark to make any of the facial features out. If this was shot in RAW, you might be able to save it by adding some fill, but I would not go too far as it will create a ton of noise. As you can see by bringing into ACR, the blue areas are where details are too dark. I know horses don’t stay still for long, so a slow shutter speed would not help.