It's possible that not all of Coerthas is covered in snow. Certainly the Central and I would imagine the Western sides are currently undergoing a permanent winter type effect, but Coethras was massive in 1.0, having a Central, Western, Eastern, Northern and Southern area. It's possible that while some of the landmass is effected by the presence of (possibly, no confirmation this is true) Shiva who may be inhabiting the Western side of Coerthas, the other areas to the South, East and Northern edges may still be green.

My personal guess is that the Southern is going to be more desolate, being in closer proximity to Mor Dhona and Thanalan after the awakening of Bahamut, that area likely got tore apart. The Eastern side may still be green, as close as it is to the Shroud and there's no winter effects there. Though that part of the Shroud, next to Fallgourd Float was torn apart by the Calamity as well, so it may not be quite so green anymore. The only section that was far enough away from the awakening of Bahamut that we currently don't have access to is the Northern (North-East in 1.0) end of Coerthas.