I'm assuming you're using log4j to generate the logs and you're saving the logs as files...
You'll have to change how you handle logs to make them work in a clustered environment. Instead of each server saving log files, you'll need to log to a shared database or use something like
Syslog. Log4J has appenders for either. You'll also want to change your log format to include the machine name / IP address so you'll know which machine in the cluster generated the log message.
As for downloading them as zip files - you'll have to create zips on the fly from whatever centralized approach you choose - you're probably doing something similar already though - I don't think there's a built in job that zips log files in Log4J.