100% correct. Just some clarification for those that don't get it. Setting cookies on mysite.com; means that the cookies will be pushed by the client for all s

100% correct. Just some clarification for those that don't get it. Setting cookies on mysite.com; means that the cookies will be pushed by the client for all subdomains for mysite.com (*.mysite.com); -- But if you're setting cookies from www.mysite.com you can serve media from cdn.mysite.com and the requests from cdn.mysite.com will not push cookies to your server.