Machining thin-walled components often suffers from dynamic instabilities like chatter due to low structural rigidity. While cryogenic support structures formed by expanding liquid CO₂ and a lubricant provide a promising stabilisation method, they introduce complex dynamic trade-offs. Specifically, sub-zero temperatures elevate workpiece material strength, leading to higher process excitation forces. Concurrently, the cryogenic cooling and ice layer shift the natural frequencies, enhancing structural stiffness. This study evaluates the critical balance between these increased excitation forces and the enhanced structural rigidity. Utilising a geometric-physical process simulation, the competing temperature-dependent effects on machining dynamics are comprehensively analysed. The results quantify how this trade-off dictates process stability, offering a predictive framework for process planning. Consequently, this work enables precise stability assessments for cryogenic-assisted thin-walled milling.