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With progressing global warming, snowfall in Antarctica is expected to increase, which could counteract or even temporarily overcompensate ice-sheet mass losses through increased ice discharge, calving and melting. For sea-level projections it is therefore vital to understand the processes determining snowfall changes in Antarctica. Here we revisit the relationship between Antarctic temperature changes and precipitation changes, identifying and explaining regional differences and deviations from the theoretical approach based on the Clausius-Clapeyron relationship. Analysing the latest estimates from global (CMIP6) and regional (RACMO2.3) model projections, we find an average increase of 5.5 % in annual precipitation over Antarctica per degree of warming, with a minimum sensitivity of 2 % K-1 near Siple Coast, and a maximum sensitivity > 10 % K-1 at the East Antarctic Plateau region. This large range can be explained by the prevailing climatic conditions, with local temperatures determining the Clausius-Clapeyron sensitivity that is counteracted in some regions by the prevalence of the coastal wind regime. We compare different approaches of deriving the sensitivity factor, which in some cases can lead to sensitivity changes of up to 7 % for the same model. Importantly, local sensitivity-factors are found to be strongly dependent on the warming level, suggesting that some ice-sheet models which base their precipitation estimates on parameterizations derived from these sensitivity factors might overestimate warming-induced snowfall changes, particularly in high-emission scenarios. This would have consequences for Antarctic sea-level projections for this century and beyond.