The phenology of plants is a major driver of agro-ecosystem processes and biosphere feedbacks to the climate system. Phenology models are classically used in ecology and agronomy to project future phenological changes. With our increasing understanding of the environmental cues affecting bud development, phenology models also increase in complexity. But, we expect these cues, and the underlying physiological processes, to have varying influence on bud break date predictions depending on the specific weather patterns in winter and spring. Here, we evaluated the parameter sensitivity of state-of-the-art process-based phenology models that have been widely used to predict forest tree species phenology. We used sensitivity analysis to compare the behavior of models with increasing complexity under specific climatic conditions. We thus assessed whether the influence of the parameters and modeled processes on predictions varies with winter and spring temperatures. We found that the prediction of the bud break date was mainly affected by the response to forcing temperature under current climatic conditions. However, the impact of the parameters driving the response to chilling temperatures and to photoperiod on the prediction of the models increased with warmer winter and spring temperatures. Interaction effects between parameters played an important role on the prediction of models, especially for the most complex models, but did not affect the relative influence of parameters on bud break dates. Our results highlighted that a stronger focus should be given to the characterization of the reaction norms to both forcing and chilling temperature to predict accurately bud break dates in a larger range of climatic conditions and evaluate the evolutionary potential of phenological traits with climate change.