It goes without saying lambs are born with wool. All animals that are supposed to walk around right after they are born and acting somewhat independent must have their coat at once since they don't just lie helpless in a pile and warm up each other.
http://www.evilempire.com/attachment.php?attachmentid=11302&stc=1&d=1268354400
I found this while looking for a priest cat (to come give last rites over the dead cat or dead squirrel / puppet or whatever the subject of this thread has evolved into).