Whether you are shooting in shutter priority or manual mode having a fast enough shutter speed to freeze your subject and create a sharp image is key!
If your shutter speed is too slow for you to freeze the motion of the horse then your image can only be blurred.
Personally I would much rather use a higher shutter speed to freeze the motion of a horse than worry about the camera deciding to use a higher ISO because its a cloudy day and so adding grain to the image, which I can remove in post processing.
There is no amount of a blurred image that can be corrected in post production because your shutter speed was too slow.
This is why i recommend to all beginners they use shutter speed priority and start out at speeds of 1250 – 1600.
These speeds are capable of freezing a galloping horse and any camera shake.
If you go out on a bright day then put the sun behind you (even if it is behind the clouds) and use the sun as your outdoor flash to light up your horse.