It would not require new animations. Some earlier robes are hoodless but quite clearly have a *DOWN* hood behind the head. It's just a folded up hood that's static.
You're probably refering to the Temple Watchman's Vest/Aspiring Knights Vest (medium armor, the latter being orange quality). I'm not sure whether the hood is animated/deformed by your movement/combat animations but will check that once I manage to log into the game. If the hood on this piece is a seperate piece as well, it could (and should) be used as a base for lowered hoods.
Edit: The hood on this chestpiece is indeed static and not animated, though I'm not sure whether a static hood will work on the chestpieces with attached capes (never used one of them myself, so no idea how badly clipping issues could be due to the cape animation).