The xdm package should provide a /var/lib/xdm directory so xdm can store its cookies there (DisplayManager.authDir: /var/lib/xdm from /etc/X11/xdm/xdm-config)
According to bug #500704, there is a new release of xorg-x11-xdm in testing for Fedora 10 that should fix this problem.
*** This bug has been marked as a duplicate of bug 500704 ***