I would like to see an ashreed hat, too. The in-game description for the ashreed you have to pick in the Sapling quest in Mournhold says that these reeds can be woven into hats, so it would be very lore-friendly to add it.
My characters:
Main and crafter: A Breton magicka templar named Erwann Sorril
Alt 1: A Bosmer sorcerer named Tuuneleg
Alt 2: An Imperial dragonknight named Gaius Tullius Hastifer
Alt 3: An Argonian vampire/nightblade named Observe-le-Xanmeer
Alt 4: A Nord werewolf/dragonknight named Sigurd Hurlevent
Alt 5: A Breton sorcerer named Gilian Sorril (he's Erwann's younger brother)
Alt 6: A Khajiit nightblade named Jolan-dar
Alt 7: A Nord warden named Sigurmar Hurlevent (he's Sigurd's younger brother)
Alt 8: An Altmer templar named Oioriel
Alt 9: An Argonian stamina Warden named Danse-avec-les-Rainettes
Alt 10: A Redguard templar named Neemokh af-Corelanya
Alt 11: A Nord stamina sorcerer named Olga Écoute-Vent
Alt 12: A Breton magicka Warden named Ian Sorril
Alt 13: A Dunmer magicka necromancer named Ilmoran Dren
Alt 14: An Orc stamina necromancer named Norgol gro-Borziel
Alt 15: A Nord magicka necromancer named Thorgen Givresang
Alt 16: An Imperial magicka dragonknight named Publius Valeirus Hastifer (Just call him "Valerio" - he's Gaius younger troublemaker of a brother)
Main in NA (For collaborative events): A Breton magicka nightblade named Titouan Sorril (long-lost brother of Erwann and Gilian)