How can I set an animated gif as user picture in OS X? Is it possible?
It isn't possible. When you specify an account picture, macOS will automatically convert the image file to
.tiff file format and save it in the cache. Unlike
.tiff is a single-image file format, so once your
.gif file is converted, the animation will be lost.
All you’ll need to do is download GIFPaper (Dropbox link).
As described in How to Use an Animated GIF as Wallpaper on Your Mac install the preference pane, and then head into System Settings. In System Settings, you’ll find the new GIFPaper option. Click it, then pick the GIF you want to use. It will automatically load up.
If you want the animated GIF as your default wallpaper, you’ll need to also add the GIFPaperAgent app to your Mac login items. Otherwise it wll go back to your default normal wallpaper when you log in again (which coincidentally is also the only way to turn it off).