Manipulation of spin ordering in oxides without extrinsic contribution is an important issue in current spintronics. This study introduced a mechanism to ascertain the formation of magnetic clusters and the magnetism of a Co-doped ZnO system by temperature-dependent magnetic susceptibility measurements. The measurements demonstrate the possibility of detecting tiny portions of Co clusters that could be created from Co oxides that were undetectable in X-ray diffraction or transmission electron microscopy. By fitting the magnetic susceptibility results, we were also able to ascertain that pure Co-doped ZnO showed a negative Curie-Weiss temperature, implying the existence of antiferromagnetic ordering; however, the Curie-Weiss temperature was gradually increased by intentional hydrogen introduction, with results suggesting that the antiferromagnetic ordering declined proportionally to the hydrogen contents by hydrogen mediation in Co-Co spin ordering and induced ferromagnetism. These results provide a useful methodological approach as well as experimental clues for identifying the origin of magnetism.