Not a hundred percent on this one Alcanallen, but the moonfull.dds is found in the Effects/weather folder. Do a search for moonfull.dds under the Effects folder in Windows Explorer to check that you do not have a duplicate tucked in another folder, like fxtextures.
Not sure that would create this square look, though. The stock moon textures are DXT5. If you hover the mouse pointer over the moon dds file in Windows explorer, a little info box pops up telling you information about what format the dds texture is in.
have you made a recent change to configoverrides or updated your version of Ankor's shaders?