Would "korpero" suffice for "body part"? Or must one use the longer "korpoparto"?

I would say korpoparto.

The problem with -er- in this context is that it usually refers to a smaller element of a whole, more dealing with composition than with parts. To me, a "korpero" would be a cell, a bit of tissue, not a whole part of the body.

I like the snow analogy. "neĝo" is a bunch of snow. A "neĝero" is a single snowflake (not a clump of snow, like a snowball). Just as a body is composed of cells, snow is composed of snowflakes.

PIV calls an "ero" an elemental piece, and I like that description.