Is it possible to have a button on the side bar to hide every open window on Ubuntu 12.04 LTS?
You can have a button to execute
wmctrl -k on to get the same effect.
I already have such a thing on 12.04 LTS in my taskbar ( classic desktop, no side-bar ).
A keyboard shortcut is always better and faster than a GUI approach.
Ctrl + Super + D will minimize all the windows on Ubuntu.
Alternatively, you can try the hot corner feature of Unity Tweak Tool, which is a GUI approach, but still very fast.
This is actually an option for the gnome desktop environment. You can select an additional entry for your desktop panel which is called 'Show desktop' and it will show or hide all windows when clicked on.
This has been available for gnome-like desktop environments since a couple of years so it should work for Ubuntu 12.04 LTS as well.
See this screenshot: