If the system is VVVF driven there is a possibility of flux failure in the bearing housing with the rotor and bearings forming the ground path, This induces a spot welding effect.
It is generally ok to cool bearings but two factors are critical, first is the chill temperature and its effect on the seals, second is the use of mechanical force on the outer or inner ring when mechanically pushed or forced into the housing, In general a cooled housing should drop in without...