Dies for cold forming (also called impact extrusion, cold forging, or cold extrusion) are always reinforced, meaning that there is an inner piece (usually called the die insert or die nib) that is reinforced by at least one stress ring (also called shrink rings). Some times the outer ring is called the die case. The inserts are interference fit into the rings/case.
Typical tool materials for die inserts are D2, M2, and M4. They are hardened and tempered to hardness of 58-64 HRC. Cemented carbides are also used, as are a range of new tool steels specifically developed for this process that have improved fracture toughness (resistance to chipping) and fatigue strength. Stress rings are made from hot work tool steels like H11 or H13 heat treated to 45-50 HRC. Punches usually start with M2 or M4 at 62-66 HRC, although cemented carbides are also commonly used.