Here is an idea for /etc/logrotate.d/xdm:
# Logrotate file for xdm.log
# The log file is named in /etc/X11/xdm/xdm-config. How to extract it here?
# DisplayManager.errorLogFile: /var/log/xdm.log
#
# Better include a warning in a comment in /etc/X11/xdm/xdm-config that the log
# file name is assumed here.
# These defaults in /etc/logrotate.conf:
# weekly
# rotate 4
# create
/var/log/xdm.log {
notifempty
missingok
}