Climate change has increased the risk of snow drought, which is associated with the deficit in snowfall and snowpack. The objectives of this research are to improve drought identification in warming climate by developing a new snow-based hydroclimatic aggregate drought index (SHADI) and to assess the impacts of snowpack and snowmelt in drought analyses. To derive the SHADI, an R-mode principal component analysis is performed on precipitation, snowpack, surface runoff, and soil water storage. Then, a joint probability distribution function of drought frequencies and drought classes, conditional expectation, and k-means clustering are used to categorize droughts. The SHADI was applied to the Red River of the North Basin (RRB), a typical cold climate region, to characterize droughts in a mostly dry period from 2003 to 2007. The SHADI was compared with the hydroclimatic aggregate drought index (HADI) and the U.S. drought monitor (USDM) data. Cluster analysis was also utilized as a benchmark to compare the results of HADI and SHADI. SHADI showed better alignment with cluster analysis results than HADI, closely matching the identified dry/wet conditions in the RRB. The major differences between SHADI and HADI were observed in cold seasons and in transition periods (dry-to-wet or wet-to-dry). The derived variable threshold levels for different categories of drought based on the SHADI were close to, but different from those of HADI. SHADI can be used for short-term lead prediction of droughts in cold climate regions and, in particular, can provide an early warning for drought in the warming climate.