The extremely low threshold voltage (Vth) of native MOSFETs (Vth~0V@300K) is conducive to the design of cryogenic circuits. Previous research on cryogenic MOSFETs mainly focused on the standard threshold voltage (SVT) and low threshold voltage (LVT) MOSFETs. In this paper, we characterize native MOSFETs within the temperature range from 300K to 4.2K. The cryogenic Vth increases up to ~0.25V (W/L=10um/10um) and the improved subthreshold swing (SS)~14.30mV/dec@4.2K. The off-state current (Ioff) and the gate-induced drain leakage (GIDL) effect are ameliorated greatly. The step-up effect caused by the substrate charge and the transconductance peak effect caused by the energy quantization in different sub-bands are also discussed. Based on the EKV model, we modified the mobility calculation equations and proposed a compact model of large size native MOSFETs suitable for the range of 300K to 4.2K. The mobility-related parameters are extracted via a machine learning approach and the temperature dependences of the scattering mechanisms are analyzed. This work is beneficial to both the research on cryogenic MOSFETs modeling and the design of cryogenic CMOS circuits for quantum chips.