That's the tricky thing with this kind of Lore, lots of speculation until Ferne or a NPC tell us it's so in game. Right now the only REAL thing we know is how the aether flow affects vegetation, the climate, and weather -- the major example being Mor Dhona. Currently we don't even know if the Paragons have met with the Gigas race and taught them to summon Shiva, as for Shiva making the weather change she would have to perpetually be summoned in Coerthas for it to again effect the aether in such a way that it causes this weather to form (snow). Let's not confuse the FC summoning of a Primal and Beastmen summoning a Primal, yes they will be similar and make the zone change (Yoshi's word) such as Ifrit causing the sky to become red, but these are temporary things that will disappear. Snow in Coerthas is the new norm as it should be with the majority of Coerthas existing in the hills and mountains in the shadow of Agalatia's Spire.