Quantum-based systems, such as quantum computers and quantum sensors, typically require a cryogenic electrical interface, which can be conveniently implemented using CMOS integrated circuits operating at cryogenic temperatures (cryo-CMOS). Reliable simulation models are required to design complex circuits, but CMOS transistor electrical characteristics at cryogenic temperatures substantially deviate from the behavior at room temperature, and no standard physics-based model exists for cryo-CMOS devices. To circumvent those limitations, this paper proposes the use of Artificial Neural Networks (ANN) and an associated training (extraction) procedure that automatically generates cryo-CMOS device models directly from experimental data. A device model for the DC characteristics of 40-nm CMOS transistors over a wide range of bias conditions, device geometries and temperatures from 4 K to 300 K has been generated and used to simulate voltage-reference circuits over a wide temperature range (4 K - 300 K). The potential application to dynamic/high-frequency circuits is demonstrated by enhancing the basic model with ANN-based nonlinear multi-terminal capacitive elements to simulate a ring oscillator. Preliminary results showing a good match between simulations and experiments demonstrate the feasibility and practicality of the proposed approach.