The interpretation of globular cluster horizontal branch (HB) morphology is a classical problem that can significantly blur our understanding of stellar populations. In this paper, we present a new multivariate analysis connecting the effective temperature extent of the HB with other cluster parameters. The work is based on Hubble Space Telescope photometry of 54 Galactic globular clusters. The present study reveals an important role of the total mass of the globular cluster on its HB morphology. More massive clusters tend to have HBs more extended to higher temperatures. For a set of three input variables including the temperature extension of the HB, [Fe/H] and M_V, the first two eigenvectors account for the 90% of the total sample variance. Possible effects of cluster self-pollution on HB morphology, eventually stronger in more massive clusters, could explain the results here derived. ; Comment: Accepted for publication in Astronomy & Astrophysics