I suspect you want to use
start
http://your.zimbra.server
Cause the start command should use your standard Windows association to launch URLs.
That doesn't work from a Win-R Run Command prompt, but it does work (for me) from a cmd *window*... and as an extra added bonus, it opened a new tab in the Firefox I had already running (this is on win2k, ff2).
Try it and see if it works for you.