Coerthas Climate Change

[Belhi]

I would put this down to Aether too. Apart from the disruption Bahamut breaking free and the pieces of Dalamud raining down on the land caused, even prior to that the proximity of Dalamud was pulling Aether out of the land. If something caused a shift to large concentrations of Ice Aether in Coerthas, it would lead to the temperature change. Its the same logic on why we have floating islands. If a particular type of Aether is particularly strong in an area it can have rather drastic effects of the surroundings.

[Berethos]

I would put this down to Aether too.

There's also how the immense amount of aether in play from Louisoix attempting to (sort of) summon the Twelve caused both healing and shifting (a bit) of other areas within Eorzea - lot of stuff going on with the aether of the land during that time.

For Coerthas, it's the fantasy version of what happened in The Day After Tomorrow, but instead of hurricane-like blizzards pulling in "super cooled" air from high in the atmosphere, it's a shifting of aether bringing in ice aspected aether that leads to a similar sort of snap freeze...though not quite as immediate (getting frozen where you stood isn't described as happening, but getting caught in rising snows or water that freezes suddenly was apparently a real threat).