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Magnetic shielding is a key technology for superconducting radio frequency (RF) cavities. There are basically two approaches for shielding: (1) surround the cavity of interest with high permeability material and divert magnetic flux around it (passive shielding); and (2) create a magnetic field using coils that cancels the ambient magnetic field in the area of interest (active shielding). The choice of approach depends on the magnitude of the ambient magnetic field, residual magnetic field tolerance, shape of the magnetic shield, usage, cost, etc. However, passive shielding is more commonly used for superconducting RF cavities. The issue with passive shielding is that as the volume to be shielded increases, the size of the shielding material increases, thereby leading to cost increase. A recent trend is to place a magnetic shield in a cryogenic environment inside a cryostat, very close to the cavities, reducing the size and volume of the magnetic shield. In this case, the shielding effectiveness at cryogenic temperatures becomes important. We measured the permeabilities of various shielding materials at both room temperature and cryogenic temperature (4 K) and studied shielding degradation at that cryogenic temperature.