A warmer climate will change the fraction of snowfall in precipitation. The switch of precipitation types not only directly changes the runoff but also influences the response of runoff to other factors, such as landscape or precipitation, which is not fully understood in previous studies. In this study, we modified the snow-involved Budyko equation for catchments with high snow ratio (the proportion of snowfall in precipitation) from the perspective of available water and energy. The elasticity of runoff derived from two modified Budyko frameworks was used to quantify the response of runoff to different factors with snow ratio and aridity index changes at 552 catchments in the contiguous USA. The results indicate that ignoring the effect of snowfall in the Budyko framework leads to overestimation of the elasticity of runoff to precipitation and landscape. With the increase of snow ratio, the elasticities of runoff to precipitation and landscape will decrease. For most catchments, the snow ratio elasticity will increase with the increment of snow ratio, and this trend is more significant in arid regions. A weak negative correlation between the snow ratio elasticity coefficient of runoff and snow ratio in humid catchments with high snow ratios are also detected. This study suggests that under the context of global warming, the decline of snow ratio will cause a more sensitive response of runoff to the changes in climate and landscape, which may result in a great challenge to the water resources management in the future.