So to apply the trayicon workaround (which works for me!

):
Locate the file webapp.ini in your Zimbra installation.
If you installed in the default location on a C: drive, it will be in the folder
"C:\Documents and Settings\[user]\Local Settings\Application Data\Zimbra\zdesktop\zdesktop.webapp"
where [user] is the user's name.
Otherwise, use "Search" on webapp.ini to get there (the older Windows Companion option may work better). Or you could right-click on the app in the Start Bar, select Properties, push "Find Target", then go up two levels to see the parent folder "zdesktop.webapp" listed. Open that to find webapp.ini.
Make a copy of the file, then use a text editor (even Notepad, though it formats it poorly) on the original to change "trayicon=true" to "trayicon=false".
Thank you to the contributors here. (But why a blue multi-? smiley

against the most useful line in the thread? I missed it first time!)