  We exploit multi-band Hubble Space Telescope photometry to investigate
multiple populations (MPs) along the red horizontal branches (HBs) and red
clumps of fourteen metal-rich Globular Clusters (GCs), including twelve Milky
Way GCs and the Magellanic Cloud GCs NGC 1978 and NGC 416. Based on appropriate
two-color diagrams we find that the fraction of 1G stars in Galactic GCs
correlates with cluster mass, confirming previous results based on red-giant
branch (RGB) stars. Magellanic-Cloud GCs show higher fractions of 1G stars than
Galactic GCs with similar masses, thus suggesting that the environment affects
the MP phenomenon. We compared and combined our population fractions based on
HB with previous estimates from MS and RGB, and we used ground-based UBVI
photometry (available for NGC 104, NGC 5927, NGC 6366, NGC 6838) to extend the
investigation over a wide field of view. All studied GCs are consistent with
flat distributions of 1G and 2G stars within ~1 arcmin from the cluster center
except NGC 416, where the 2G is more centrally concentrated. 2G stars of NGC
104 and NGC 5927 are more centrally-concentrated than the 1G, whereas the
distribution is flat for NGC 6366 and NGC 6838. We discover that most of the
analyzed GCs exhibit extended sequences of 1G stars along the red HB, not
consistent with a simple population. The comparison between appropriate
synthetic and observed CMDs reveals that these extended distributions are
consistent with either star-to-star variation in helium or with an internal
metallicity spread, recalling the inhomogeneity of 1G stars along the ChMs.
