Context. Previous studies of the initial conditions of massive star and star cluster formation have mainly targeted infrared-dark clouds (or IRDCs) toward the inner Galaxy. This is because IRDCs were first detected in absorption against the bright mid-infrared (IR) background of the inner Galaxy, requiring a favorable location to be observed. By selection, IRDCs therefore represent only a fraction of the Galactic clouds capable of forming massive stars and star clusters. Owing their low dust temperatures, however, IRDCs are bright in the far-IR and millimeter and, thus, observations at these wavelengths have the potential to provide a complete sample of star-forming massive clouds across the Galaxy. Aims. Our aim is to identify the clouds at the initial conditions of massive star and star cluster formation across the Galaxy and compare their physical properties as a function of Galactic longitude and Galactocentric distance. Methods. We have examined the physical properties of a homogeneous Galactic cold core sample obtained with the Planck satellite across the Galactic plane. With the use of Herschel Hi-GAL observations, we characterized the internal structure of the most reliable Galactic cold clumps within the Early Cold Core (ECC) Planck catalog. By using background-subtracted Herschel images, we derived the H 2 column density and dust temperature maps for 48 Planck clumps covered by the Herschel Hi-GAL survey. We calculated and analyzed the basic physical parameters (size, mass, and average dust temperature) of these clumps as a function of location within the Galaxy. We also compared these properties with the empirical relation for massive star formation previously derived. Results. Most of the Planck clumps contain signs of star formation. About 25% of the clumps are massive enough to form highmass stars and star clusters since they exceed the empirical threshold for massive star formation. Planck clumps toward the Galactic center region show higher peak column densities and higher average dust temperatures than those of the clumps in the outer Galaxy. Although we only have seven clumps without associated YSOs, the Hi-GAL data show no apparent differences in the properties of Planck cold clumps with and without star formation.