So many thoughts here and only a few minutes.
You shot these, at least the first one, at 1/200th which is no where near fast enough for cutting. You have to be at least at 1/500th for cutting, even faster would be better. Not only is your first shot not fast enough shutter speed, it is underexposed. You've lost shadow detail on the horse. (Look at the horse's neck and belly)
So, yes, as the other poster's pointed out this is subject motion not missed focus.
Up the ISO. There is no way I could ever shoot an indoor show at ISO 800. Or even 1600. I am almost always at 3200. Sometimes, 6400.
Which means, unfortunately, your F/4 lens is not going to be fast enough. You are probably looking at a fast prime if you want to continue to shoot NCHA or other indoor horse events.
You had mentioned the bright ambient light coming in and it is good that you picked up on this. Open overhead doors or windows with throw your exposure off every time if you use your in-camera meter. I always use a hand held incident meter to get my exposure and set it and leave it. Failing using a hand held meter, do some test shots and get a proper exposure and use that. If you use your camera in one of the program modes every time a horse runs in front of one of those doors it is going to get fooled and give you and underexposed shot. DO NOT USE THE HISTOGRAM. That is going to show you the overhead door as blinkies. You want the doors to be blown out.
If you are not already familiar with one, you are going to have to become very intimate with a noise reduction program.
HTH