with logwatch you can send now a summary of all logs which are searched per mail.
It would be nice, if you could config that the logfiles which are scanned could be send per mail as attachment, but only the entries in the date range.
I don't think that logwatch is the right tool for that purpose. It's for analyzing not for distribution of logs. And SMTP isn't the right protocol to send (or distribute) data: The overhead is too big and the size of a message is often restricted to few MBs.