well for starters, get rid of the -'s inside the brackets. $_SESSION[‘mySession_name’] would be the correct way to reference it.
Try putting this into your echo script:
session_set_cookie_params(0, '/', '.dot.kr');
session_start();
var_dump($_COOKIE);
echo $_SESSION['mySession_name'].'<br>';
and see what it tells you in each subdomain.