Heat pump adoption in cold climates is limited by various technical challenges, including heat capacity degradation, compressor deterioration, and frost accumulation on the outdoor heat exchanger. Furthermore, widespread adoption of heat pumps with high global warming potential presents a possible environmental concern. Thus, we present a heat pump concept termed the "saturation cycle," which uses numerous compression stages to improve energy efficiency and injects two-phase refrigerant between compression stages to dramatically reduce compressor discharge temperatures. Given the growing interest in heat pumps, there is a need for a straightforward framework for parametric evaluation of natural refrigerants in high-efficiency heat pump cycle architectures, like the saturation cycle, in adverse climates. This study develops a thermodynamic modeling framework and focuses on the application of natural refrigerants to explore the performance trends at extremely cold climates down to -25 degrees C. This study shows that a two-stage saturation cycle and four-stage saturation cycle can reduce the compressor discharge superheating by up to 51-57 % or 73-80 %, respectively, depending on the refrigerant. Furthermore, at -25 degrees C, a two-stage R-290 saturation cycle heat pump theoretically can use 25 % less power than a single-stage heat pump or can provide up to 59 % more heating capacity when using the same compressor power as the baseline single-stage heat pump. The exergetic parametric analyses show that twophase refrigerant injection fundamentally improves the thermodynamic performance of the heat pump, reducing overall exergy destruction by 10 % compared to a vapor-injection heat pump, compared at -25 degrees C. Thus, the saturation cycle is a promising heat pump cycle architecture for cold climate applications due to its superior energy savings (or capacity improvement) and substantial de-superheating capabilities.