dark headed animals are a pain! Especailly in (what looks like) dimmer overcast lighting and when moving!
See the dark areas effectivly need one of two things
1) direct lighting - good light on them to show the details up
2) overexposure - using a slower shooting speed/wider aperture to get a slight overexposure on those areas when the lighting is less than idea.
Both things you didn't really have access to in this case since the sun is hidden and the shutter speed needs to be kept fast to freeze the motion - probably the only way round this would have been to use fill flash to give more light to the foreground areas and thus the darker parts of the horse