My Debian system is very short on RAM so I've shutdown the logger service, so it's tricky for me to check this one.
However, to cover some basic ground, try running this as the zimbra user:
Code:
zmlocalconfig | grep smtp_destination
That will show where the log is being mailed to, if anywhere. If there's an address in there, is it what you expected it to be?
EDIT:
Hang on, I just re-read your post, when you say 'logwatch' are you refering to the log section of Zimbra, or a third party app ?