1. Grandsire. Grandsire is always the sire of the horse's sire.
2. Grandam. Always the dam of the horse's sire.
3. Damsire. The sire of the horse's dam.
4. Second dam. The dam of the horse's dam.
As you can see, we distinguish the sire's side of the pedigree from the dam's or "distaff" side. Many horse breeders believe that the mare gives more to the foal than the stallion. This may be true at two levels - first in that the dam provides the vital mitochondrial DNA and second in that horses are higher mammals and the foal learns from the dam's behavior. A good horseman never breeds from a mare with a bad temperament...
But if you use grandsire to refer to the father of a horse's mother, you'll be exposed as a noob.