It is becoming recognized that the behavior of electrons in hydrogen-bonded systems is far more complicated than previously thought. One key problem would be its relation to the local/extended nature of molecular dipole, i.e., whether it is a true "molecular" property. The present study shows, on the basis of analyses of electron densities in water clusters, that the dynamical molecular dipole of water is not enhanced, and is even reduced, upon hydrogen-bond formation because of the electrostatic dragging effect of the electrons of surrounding molecules. As for the static molecular dipole, intermolecular charge transfer occurring upon hydrogen-bond formation is responsible for a significant part of its enhancement. The large difference between these two types of molecular dipole suggests that, for better understanding of the terahertz and dielectric properties of hydrogen-bonded water, where the dynamical molecular dipole is directly involved, the extended nature of the molecular dipoles should be taken into account.