Cattle:Herd::Horses:

Stud

The correct analogy is:

Option 3: Stud

Explanation: The analogy "Cattle:Herd::Horses:Stud" relates to the collective noun used for a group of horses. Just as "herd" is used for a group of cattle, "stud" is used for a group of horses, especially when referring to a group of horses kept for breeding purposes.