Cryogenic electronics manufactured using conventional CMOS processes but operated at temperatures of 4 K have recently attracted interest as low-noise amplifiers and precision controllers. The neutrinoless double beta decay experiment CUORE operates 988 individual detectors at base temperatures of about 10 mK but uses room temperature electronics for sensor readout. The next-generation experiment CUPID (CUORE Upgrade with Particle ID) will build upon CUORE's cryogenic infrastructure, providing an opportunity to upgrade the electronics chain. CMOS microelectronics operated at temperatures as low as 100 mK or below offer an alternative approach to signal preamplification in CUPID, but there exists little prior work exploring CMOS device characteristics in this temperature region. We present a characterization of 180 nm CMOS technology down to 100 mK, which can be used to inform the design of cryogenic electronics for a variety of applications, including deployment in CUPID.