Max' clothing habbit (linking to wizard of oz)

I've read through quite a few of the other threads, and noticed that the wizard of oz link has already been brought up. This is my take on it, don't know if I'm overanalyzing a bit...

the two more obvious links are:

Lion = Lion, no courage for having left his wife and child.
Scarecrow = Both, no brain, not very smart. They both call themselves scarecrows in one scene.

Now I think max' clothing habbit, of being cold and calling himself heartless can be seen as a parallel to the tin man. Metal is generally cold and Max says he is cold blooded. Tin Man has no heart, so this may be the reason why Max wears so many layers of clothes??

With Lion and Scarecrow the links are quite obvious, but how else could a parallel between max and the tin man have been made???