As global deployment of electrochemical energy storage accelerates to support renewable energy integration, infrastructure in cold regions faces unique electrolyte leakage hazards that threaten operational safety and environmental integrity. This review synthesizes critical mechanisms governing electrolyte seepage under subzero conditions, where cryogenic temperatures induce phase separation (e.g., salt precipitation in Li-ion carbonates, vanadium hydrate crystallization in flow batteries) and material embrittlement, exacerbating containment failure. Leaked electrolytes exhibit multiphase transport dynamics dominated by freeze-thaw cycles: ice formation restricts vertical leaching but generates anisotropic migration pathways through unfrozen brine channels and frost-heaved soil cracks, while thermal gradients drive directional contaminant spread via solute exclusion and Soret effects. Physically based models (SHAW, CoupModel, Hydrus-1D) simulate these coupled thermo-hydrochemical processes, integrating Clapeyron-driven phase transitions and non-Arrhenius ion transport scaling. However, knowledge gaps persist in quantifying interfacial electrochemistry at ice-electrolyte boundaries and predicting multicomponent cross-drag in frozen matrices. The analysis establishes a foundation for designing cryogenic-resilient containment systems, addressing urgent safety and environmental challenges for energy storage in cold climates.