Illustrator 10 files do have built in compression. When you Save As... and click save, you are presented with a few options, one of which is compression.
If you would rather use WinZip, then turn this off first, because they both use similar compression algorithms, and therefore, cannot make any significant improvement on an already compressed file. However, you would probably be better off leaving this option on and forgetting about zipping it, because it cuts out one whole process, saving time for you and whoever else might need to open your files.