www.mysite.com and mysite.com SHOULD be the same domain, in fact, most hosters (the good ones anyways) don't care if you provide the www. or not when typing in their URL, it should load either way.
Of course, I've got invincible cookies atm, so I'm not the cookie expert :-)
One idea? Set the cookies available for all areas...
setcookie ('name', "value", time()+600, '/');
setcookie ('name', "value", , '/');
top one being if you use a timeout cookie (set for 10 mins)