If you were a Mac user in the 1990s, you may remember the charming mascot-like icon Clarus the Dogcow that began life as part of the Cairo font and later came to be used in the Page Setup dialog box for printing in Mac OS. (See here
for a run-down of the history.)
I've just been digging around inside Twitter for Mac, and I've discovered a hidden reference to ol' Clarus. There is an alternate icon with the filename birdcow.icns.
To find this icon, you'll need to first find the Twitter app in Finder (or you can use Terminal - but if you know about that, you don't need me to tell you how). Next, right-click on the app and select "Show Package Contents." Then open Contents->Resources and scroll down to find the birdcow icon, which can be opened in Preview.
If you'd like to make this the default icon, there are two things to do:
(1) Select the Twitter app and use the Get Info command (press Command-I). Change the "Sharing and Permissions" for everyone to "Read and Write" (you can change back afterwards). Open up the birdcow.icns file. Choose "select all" then "copy" in Preview with the birdcow window in the foreground. Then click on the Twitter icon in the top left of the Get Info box. Type Command-V to paste the new icon on top.
(2) Assuming you'd like the application to internally use the new icon, you'll need to modify the Info.plist file (in the Twitter.app/Contents directory). The easiest way to do that is to open the file in TextWrangler and find the line that says "<key>CFBundleIconFile</key>". Right below that should be the filename of the current icon in use, wedged between "<string>" and "</string>". Replace that filename with birdcow.icns, then you'll have yourself a new, retro-styled icon that harkens back to the early days of the Macintosh.
Incidentally, I have now changed my avatar from Clarus the Dogcow to this stylish Birdcow.