I believe the cornett used to be made of ram's horn - hence the name.

Ibex horn, maybe. The shape is nothing like a ram's horn, nor is the sound anything like a musically-adapted ram's horn (the shofar). It's more like a trumpet with vent holes. Most surviving and reproduction cornetts are made of wood (either one-piece or glued-together strips).

Some old wooden cornetts have bumps carved into them to simulate the appearance of an ibex horn.