This study presents an energy and exergy analysis of two geothermal systems, namely a shallow Ground Source Heat Pump (SGHP) and a Deep Geothermal Energy (DGE) system, for supplying the heating demand of a greenhouse located in the cold region of Meshginshahr, Iran. The thermodynamic modeling was carried out using Engineering Equation Solver (EES) based on real data from the Sabalan geothermal field. Under design conditions (outdoor temperature of −10 °C and indoor temperature of 20 °C), the greenhouse heating load was calculated to be 126 kW. The results indicate that the SGHP system, utilizing soil at an average temperature of approximately 10 °C, achieves a coefficient of performance (COP) of about 3.5 and an exergy efficiency of 0.62. In contrast, the DGE system, with a geothermal fluid inlet temperature of 85 °C, demonstrates superior thermodynamic performance, reaching an equivalent COP of around 20 and an exergy efficiency of 0.68. This performance improvement is primarily attributed to the higher source temperature and the significantly lower electrical energy requirement in the deep geothermal system. From an economic perspective, although the shallow geothermal system benefits from simpler implementation and lower infrastructure requirements, leading to a shorter payback period, the deep geothermal system offers more stable long-term performance due to its minimal electricity consumption and reduced operational costs. Furthermore, the findings highlight that source temperature conditions and thermal properties of the surrounding environment play a critical role in determining the overall system performance.