Snowmelt is a vital contributor to river discharge across the Northern Hemisphere, supplying freshwater to over 1.5 billion people and supporting key economic sectors such as agriculture and hydropower. However, climate change has led to a decline in snow water equivalent (SWE) on almost the entire Northern Hemisphere, reducing snow-based water availability. Despite the importance of snowmelt and the pressure imposed by climate change, no large-scale studies have examined the connection of snowmelt dynamics and river discharge beyond statistical measures, which fail to capture the complexity of hydrological regimes. To address this gap, we perform causal discovery using PCMCI, a method that adapts the PC proposed by Peter Spirtes and Clark Glymour to the time series setting, to obtain qualitative causal structure across 119 basins from 1980 to 2022 and then quantify using causal effect estimation with a 20-year moving window and a random forest estimator. Our results show that the role of snowmelt in streamflow generation is changing. In various basins where the method allows for trend detection, the ratio of the causal effect of snowmelt on river discharge to the mean of the river discharge is increasing despite declining SWE. This suggests that as precipitation patterns shift and intra-annual variability increases, snowmelt may become more important for streamflow generation in certain basins despite a generally declining SWE. While regional differences emerge, causal effects do not consistently correlate with geographical factors such as latitude or basin characteristics. Analyses in six basins that serve as illustrative examples, indicate that changes in seasonal hydrology, particularly the timing and distribution of precipitation, influence the relative role snowmelt plays for river discharge. These findings highlight the power of causal inference over conventional statistical measures in enhancing the analysis of large-scale snow hydrological regimes by adding depth to existing approaches.