This mod makes it possible to wear face masks on characters with facial hair without the beard clipping into the mask. Skyrim normally doesn't have any designated slot for long beards, which is why the Shrouded Cowl only has the mask for female characters in vanilla.

Files for adding the missing mask to the Shrouded Cowl are provided in addition to the engine fix. You can make this work for any item that covers the face by adding slot 44 to its Armor form.