Or another very easy way:

1. open new empty mail (CTRL+M)
2. Paste into the body mail this:
   opera:/button/Hide%20opera%2C%201%2C%2C%22Hide%20Opera%22%2C%20Opera%20Logo
3. Close it
4. Open Drafts and find that closed mail and click on that link in it's body
5. confirm adding new button
6. in new opened window go to 'My Buttons' in 'Buttons' TAB
7. and use drag&drop for put the newly created 'Hide Opera' button on the panel to which you want

try this: http://opera.customize.general.narkive.com/QVE9Ve3s/toolbar-button-for-minimize-to-tray