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Abstract The cold point tropopause, the minimum temperature within the tropical upper troposphere‐lower stratosphere region (UTLS), significantly impacts Earth's climate by influencing the amount of water vapor entering the lower stratosphere. Understanding which mechanisms are most important in setting the cold point temperature and height may help us better predict how it will change in a future warmed climate. In this analysis we evaluate two mechanisms that may influence the cold point—cold point‐overshooting convection and the radiative lofting of thin cirrus near the cold point—during boreal winter by comparing 30‐day global storm‐resolving model (GSRM) simulations from the winter phase of the DYAMOND initiative to satellite observations. GSRMs have explicit deep convection and sufficiently fine grid spacings to simulate convective overshoots and UTLS cirrus, making them promising tools for this purpose. We find that the GSRMs reproduce the observed distribution of cold point‐overshooting convection but do not simulate enough cirrus capable of radiative lofting near the cold point. Both the models and observations show a strong relationship between areas of frequent cold point overshoots and colder cold points, suggesting that cold point‐overshooting convection has a notable influence on the mean cold point. However, we find little evidence that the radiative lofting of cold point cirrus substantially influences the cold point. Cold point‐overshooting convection alone cannot explain all variations in the cold point across different GSRMs or regions; future studies using longer GSRM simulations that consider longer‐term UTLS processes are needed to fully understand what sets the cold point.