The picture is saved as a GIF when uploaded to SkyDrive, but when shared via other means (e.g. e-mail) it's converted to a JPG and the animation is lost. So, you just need to get it to SkyDrive first and then you can share that file anyway you want (obviously, the viewer needs to be able to display animated GIFs properly).
Note: My phone is automatically set up to save pics to SkyDrive, but I assume it will work the same when done manually.