Is it possible to use cookie-free domains in WordPress?

Earlier it wasn’t possible to use cookie-free domain while using Cloudflare CDN/ Proxy to be exact. Well until yesterday. Cloudflare rolling a new update where they are retiring _cfduid cookie, so your best option will be to wait a few weeks.

More details on this-
https://blog.cloudflare.com/welcome-to-privacy-and-compliance-week/#improving-the-privacy-of-our-service