It's relevant for Winter Burial which adds splash to your Glacial Hammer... Would Pulverize then work to increase main hit's damage (and of course also the splash)?
Melee Splash Support will not add any tags. Neither does Arcane Surge. No supports add tags.
Melee Splash Support will add splash damage to a strike skill, which is area damage. Since the strike then has the property of dealing area damage, it would become suportable by Pulverise Support. That has nothing to do with tags.
Puverise Support's damage bonus only affects area damage. The splash is area damage, the direct hit that causes the splash is not. So that modifier only applies to the splash damage.
Because Glacial Hammer has a threshold jewel that adds an area component, it is always supportable by Pulverise supports that apply to skills with area. This is because threshold jewels being added and removed can't change supportability of gems, so gems get the necessary supportability by default.