Notice the overall underexposure of your first posted image. The EXIF data shows a -.7 bias, which to me means the camera underexposed the image by 2/3 of a stop. This fact would account in part for the horse having little detail and tonality.

Keep it simple. Set the ISO to 400 (or perhaps 800). Put your camera on Shutter Speed Priority, and set it for, say 1/200 sec. This SS should stop the motion of horse legs strutting. The camera will select the Aperture.

Set the camera for Evaluative Metering. This setting will read the whole scene for setting exposure.

At some distance, even a large aperture like f/2.8 will tend to keep the main subject in focus showing sharp detail.

With these settings, the camera will of course try to expose the scene for an 18-percent gray tone (thereby producing an underexposed image). So set the Exposure Compensation to +1 or +1.5. Experiment with the EC.

These settings will also work for photographing airborne aircraft and for objects in snow or bright sand (except you'd likely start with a lower ISO setting). The same circumstances of a dark subject against a bright field will prompt the camera to underexpose the main subject. Ride the EC to gain a good exposure under these circumstances.

The histogram of an image will tell you if the exposure values have been adequately captured. In the histogram, you should see the displayed values reaching the rightmost part of the graph without touching or bunching up against the right side of the graph.

Learn the histogram if you haven’t already. It informs you of the image exposure. This Web page presents a useful explanation of the histogram in photography: http://www.luminous-landscape.com/tutorials/understanding-series/understanding-histograms.shtml