We address the problem of the horizontal branch (HB) morphology in Galactic globular clusters, and specifically the extent of the HB and the presence of blue tails. We defined a set of new parameters describing the HB morphology, which supplement the standard Dickens type and the Lee-Zinn parameter (B - R)/(B + V + R). We measured these new parameters for a set of 53 clusters, and combined them with the structural and other parameters taken from the literature. We then performed an extensive statistical analysis of this data set, and identified several interesting new correlations. Our principal result is that the net length of the HB, and the presence and extent of the blue tails in particular, are correlated with the cluster density and concentration, in the sense of more concentrated or denser clusters having bluer and longer HB morphologies. This effect is especially strong for the intermediate metallicity clusters, which should be the most sensitive group, according to a simple theoretical arguments presented here. Thus, the cluster environment can affect the stellar evolution leading to the HB, and therefore the HB morphology. We interpret this result in terms of an enhanced mass removal from the HB progenitors, possibly due to an increase in interactions between stars in denser cluster environments. We see some evidence that lower metallicity stars lose a smaller fraction of their mass as they evolve towards the HB. Whereas the exact dynamical mechanism for the enhancement of the mass loss remains unclear, it is apparent that the dynamical evolution of stellar systems can affect their stellar populations. This is consistent with the evidence on stellar population gradients in globular clusters, discovered previously.