The shutter speed is too slow and you are getting motion blur, for horses (or action in general) you want to be somewhere north of 1/1000s.
The classic lens for this would be a 70-200 f/2.8 as you need as much light (fast aperture) as possible so you don't have to bump the ISO too high. As you say, the 150-600 is pretty slow aperture unless you are in bright sunlight, which this shot isn't. The simple solution is to bump up the ISO.