Is there a word for the leather that covers a dead person's face? I am pretty sure there was a word for that, but I can't remember what it was.
I've never heard of leather specifically, or even of just the face being covered, but a general term for something that a corpse is wrapped in is a shroud:
: a sheet in which a corpse is wrapped
: a shroud for the dead
especially : CERECLOTH —usually used in plural
: cloth treated with melted wax or gummy matter and formerly used especially for wrapping a dead body
Never heard of leather either...
There are death masks made of wax or plaster....
But I think it is more likely that the word you are looking for is not for bodies' heads but babies'... a cawl
A caul or cowl is a piece of membrane that can cover a newborn's head and face.