Yoshi's Saddle Is A Shell
So as I have mentioned a few times before, the saddle of Yoshi's back is not part of his body, but well a saddle that is also a shell.
This detail has been mention a few times before. One Takashi Tezuka had mentioned it on page 13 of the Super Mario All-Stars Limited Edition Wii booklet. "That saddle you see on his back was actually his shell.".......
It was also brought up in Nintendo Kids Space of The Nintendo Co. Ltd. "He has a shell on his back."
This is also why when Baby Yoshis hatch from eggs they don't have shells on their back, because it's not part of their body. Which makes sense because shells are basically clothes. Now Baby Yoshis can put on a shell afterwards, but they typically don't.
So yeah, Yoshi's saddle is a shell. Written by Eris the Lorekeeper.