Characterization and modeling of CMOS devices at 4.2 K are carried out in order to simulate low-temperature operation of CMOS circuits for Josephson-CMOS hybrid systems. CMOS devices examined in this study have been fabricated by using 0.18 μm, 0.25 μm, and 0.35 μm commercial CMOS processes. Their static I-V characteristics and capacitances are measured at 4.2 K to establish the low-temperature device model based on the BSIM3 SPICE model. The propagation delays of CMOS inverters measured by using ring oscillators agree well with the simulation results. The experimental results indicate about 40% speedup from 300 K to 4.2 K. A three-transistor DRAM cell for a Josephson-CMOS hybrid memory is also investigated at low temperature. The temperature dependence of the retention time shows an exponential increase at low temperatures. Based on the low-temperature CMOS device model, we have developed short-delay CMOS amplifiers, which would amplify a 40 mV voltage input to CMOS voltage level with the propagation delay of about 100 ps, assuming the use of a 0.18 μm CMOS process. We have measured the propagation delay of the CMOS amplifier by using a single-flux-quantum (SFQ) delay measurement system. This is a complete demonstration of the signal exchanges between SFQ and CMOS circuits at 4.2 K.