More "flowy", yes. I think I've seen a comic book woman wearing something like that, covering even her face, but I can't remember where.
I feel like it's a common trope but I'm not seeing the things I'm thinking of.
The White Court is Etruscan in origin, it is the language they choose to converse in. The Etruscan’s had their own version of the Fates, same beings different names to the Greek.
What if the cloth was a gift from the Fates? A Ravelling as opposed to an unravelling. Given that The Queens of Faerie are inheritors of the Greek Fates (amongst others) it may explain what Winter wants with an alliance with the White Court, they are revisiting an old association. Oh and the God of War in the Etruscan Pantheon, the Ares equivalent is Laran.
I think that the White Court arise out of something that happened in relation to Erus (Eros) and Psyche, the original Whamp being a scion of them or their daughter Volupta/Hedone corrupted somehow. Psyche is depicted with butterfly wings (Psyche is Greek for butterfly) it’s no accident that is how we see Thomas depicted in Grave Peril.
I've had a hard time finding anything specific to Etruscan or Roman mythology, but there's one thing that might be quasi-relevant.
The Velificatio effect.In the real world, it's just an artist's stylistic device used to denote divinity or royalty. It means "vigorous movement," or "the vault of heaven," both of which would be good to describe mobile garments made to defend the wearer.
Maybe in the Dresdenverse the motif and name was inspired by real fabric that powerful beings possessed. And as the White Court royalty, House Raith acquired some?