Another thing: use the trayicon plugin.
Goto (hopfully translated correctly, running german UI here) <File> <Configuration>, click "Load" and selece trayicon.so.
Then <File> <Configuration> <Setting>. There you will find a new topic Plugins. Select TrayIcon and mark all checkboxes.

Now claws'll start minimized and will close itself to the statusbar.
If you wanna quit the program do it via <File><Exit>.