The session itself has little to do with your domains.
1) The session is identified by a cookie with the session id (or passed in the url).
2) The cookie has to do with domains: you can make a cookie to be accessible in subdomains, but for that you will probably need to modify a php ini setting (session.cookie_domain)
3) And now let's suppose that the subdomain is hosted on the same server, and you don't need to share session data between hosts - you still have to be careful not to override gathered session.
Read these for more details, and you will get the point: