I have no idea for how to do this using Webmin, but the rsyslog daemon shipped with Ubuntu has the capability to accept connections and log events from remote machines. You can enable it by adding the following lines to /etc/rsyslog.conf:
# provides UDP syslog reception
# provides TCP syslog reception
Then on other Linux boxes you can put the following into /etc/rsyslog.conf to enable remote logging:
The Windows machines and Cisco devices will have their own mechanism for forwarding their logs to the remote syslog server.