The Zimbra install suggests that you do not want to use a firewall. Actually, this is not the wisest decision, you should have a firewall. Ubuntu 8.04 (Zimbra does not support 8.10 yet)
One thing that is important to recognize in regard to the UFW firewall is that there are already several common rules that are configured into the firewall immediately. One of those is the state rules that provide for any RELATED or ESTABLISHED connections. This means that if you connect to a web server from a machine it will allow the information you requested from the web server to return based on the fact that the local machine established the connection and the returning information was related to that request.