Please show me your face.

That black hooded-cloak Zelda wears is not appropriated for mourner either, because people who dresses in black for federals do not looked like that and they don't need a scarf. It is too heavy and over-sized actually a weather cloak, what did you expect that she's wearing a scarf for? It meant to keep her warm and prevent the chills from both rain and snow because Hyrule Castle is always covered in dark ever-raining storm clouds since the invasion and the tower she's been locked in is empty and very cold has has a barred (glass-less) window, lots of holes/cracks in walls and barely had enough fire-wood. Either that or to hide herself for three reasons; 1 the fact she's born physically deformed like Quasimodo (which she's not), 2 to protect her identity (if only she escape early just like OOT!Zelda did, and at the same time her own people now hated her and called her a traitor/coward and they think that she choose to surrender means 'she willingly sold her own country to the enemy to save only herself and no one else'), or 3 meant to hide an multitude of horribly fresh scars and injuries left untreated that made both her face and body physically deformed (when received them from Zant's attacks)...that makes more sense!