Climate change is expected to increase the occurrence of droughts with the hydrology in alpine systems being largely determined by snow dynamics. In this paper we propose a methodology to assess the impact of climate change on both meteorological and hydrological droughts taking into account the dynamics of the snow cover area (SCA). We will also analyse the correlation between these types of droughts. We have generated ensembles of local climate scenarios based on regional climate models (RCMs) representative of potential future conditions. We have considered several sources of uncertainty: different historical climate databases, simulations obtained with several RCMs, and some statistical downscaling techniques. We then used a stochastic weather generator (SWG) to generate multiple climatic series preserving the characteristics of the ensemble scenario. These were simulated within a cellular automata (CA) model to generate multiple SCA future series. They were used to calculate multiple series of meteorological drought indices, the Standardized Precipitation Index (SPI) and Standardized Precipitation Evapotranspiration Index (SPEI)) and a novel hydrological drought index (Standardized Snow Cover Index (SSCI)). A linear correlation analysis was applied to both types of drought to analyse how they propagate and the time delay between them. We applied the proposed methodology to the Sierra Nevada (southern Spain) where we estimated a general increase in meteorological and hydrological drought magnitude and duration for the horizon 2071-2100 under the RCP 8.5 emission scenario. The SCA droughts also revealed a significant increase in drought intensity. The meteorological drought propagation to SCA droughts is reflected in an immediate or short time (1 month), obtaining significant correlations in lower accumulation periods of drought indices (3 and 6 months). This will allow us to obtain information about meteorological drought from SCA deficits and vice versa.