The deformation behaviour of metals and alloys is significantly affected by both stacking-fault energy and processing temperature. By lowering the former, deformation twinning is favoured over dislocation slip, whilst cryogenic processing partially suppresses dynamic recovery. Three materials having different stacking-fault energies, that is, Al AA1050 (high), pure Cu (medium) and Cu-15Zn alloy (low) were rolled at room (RTR) and at cryogenic (CR) temperatures up to a true strain equal to 1.5. Annealed coarse-grained samples were tested in tension at room and cryogenic temperatures. The processed samples were characterized by optical and transmission electron microscopy, hardness measurements and room-temperature tensile tests. CR increases the tensile strength with respect to RTR for the three materials; elongation to failure is decreased for AA1050, whilst for Cu and Cu-15Zn the CR effectively increases the ductility. Cu-15Zn sample after CR exhibits a microstructure relatively heterogeneous, suggesting static recrystallization events in the temperature excursion from 77 to 298 K. Finally, it was concluded that cryogenic deformation increases strength, whilst low SFE increases the ability to absorb plastic deformation, an effect strongly increased at cryogenic temperatures. The present investigation gives some basis for the development of cryogenic severe plastic deformation processes.