Bearing Installation

I think it is more common to freeze the shaft. This will allow a tighter interference when the temperatures normalize.

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 force otherwise there are potential fractures due to the embrittlement of the bearing metal.

As janderson says, for typical industrial machinery with rotating inner ring and stationary outer ring, the tighter interference fit is usually on the shaft, not in the housing.