I sorted out this problem now
Here was my soloution.
if ($host ~* www(.*)) {
set $host_without_www $1;
}
add_header Set-Cookie
"logged_in=1;Domain=$host_without_www;Path=/;Max-Age=315360000";
Posted at Nginx Forum: https://forum.nginx.org/read.php?2,269189,269190#msg-269190