By default, file or program shortcuts you add to the start menu use the icon of the target application, or the icon corresponding to that particular file type. But the shortcut is independent from the target file or program itself, which means that rename or change its icon to anything you want. (Making all start menu items use the same icon is a great workaround for a start menu opening slowly, for old machines or PCs mostly used through remote desktop connections!)
Behind-the-scenes, the start menu is just a shortcut display tool that combines the public start menu and the start menu for your profile. To make changes to t global start menu items, Windows 7 will require the administrator's password (unless you changed your User Account Control settings). But you won't need special permissions to edit file shortcuts or programs you added yourself.
First, find the shortcut whose icon you want to change (either navigate to it, or type its name in the search field). I have two versions of the Opera web browser installed on my PC: to easily distinguish between the Classic and new versions, I'll rename the old one and change its icon. Once you found your shortcut in the start menu, right-click on it and choose "Properties" (bottom).
The Properties dialog opens, with the Shortcut tab selected by default. To rename the shortcut, select the General tab instead. In the first text field, type over the existing shortcut name. If that's all you wanted to do, click OK and enter the administrator's password if prompted to do so. Changing the shortcut's icon is done from the Shortcut tab: select it if needed, and click on Change Icon the button at the bottom (see the next screenshot).
A Change Icon popup will open, showing a system or program path in the text box under Look for icons in this file. That's because Windows programs contain icons embedded into the executable file. Look at the icons offered: if they come from the target program or file itself, and you don't like any of them, erase the value in the text field and hit Enter to see the default icons. Double-click on an icon to use it. Click OK to use that icon, and click OK once more to save.
Bonus Tips - advanced shortcut options:
From the Shortcut tab, you can force the shortcut to run as administrator (click on the Advanced button). Clicking the Open File Location button will open in Windows Explorer the folder that contains the target program or file. And the Run dropdown menu lets you force the program to open maximized / minimized when it launches (that setting only works for windows that can be resized). And you can start a program with a keyboard shortcut from that same screen!