I would expect that unless you have exceptionally large cookies, the saved roundtrips from another TLS handshake matter more than the data transmission for the cookies.
For assets served from a third party (a CDN), you don't want to send cookies that might include secrets (a session cookie that could allow access to a user's account for example).
You can trust that a third party won't intentionally log or make use of any sensitive information in cookies but you can't guarantee it. Best not to send it at all.
Won't that naturally be on a different domain anyway?
How much performance hit do cookies really have in 2023?
But the motivation to put stuff on a CDN would be to improve performance. If you put your HTML on your own HW and your assets on a CDN for performance reasons, you might want to check if that really pans out, because those extra roundtrips may kill all performance savings you get from the CDN.