Based on some testing in our staging environment, it does not appear that XF will rewrite cookies when the config['cookies'] block changes. So users that previously have a cookie set for www.example.com do not have their cookie updated to .example.com. Thus, the only way I've been able to get the session cookie on the subdomain is to logout and login again to start a new session with a new cookie being set.
Since this logout/login song and dance will be a bit of a nuisance, I'd like to find a way to automate this server-side. Any thoughts on what I might need to hook into in order to check for www.example.com session cookies and rewrite them to .example.com? Obviously the user will need to visit www.example.com first to get this rewrite to happen, but that won't be a problem in our case.