Snow water equivalent (SWE) is a routine output from reanalysis systems and offline land-surface schemes, but documented discrepancies among the resulting SWE products impede the assessment of hemispheric-scale snow mass variability and trends. We investigate SWE differences between three modern reanalysis products (ERA5, JRA-55, and MERRA-2) from 1980-2020 by creating reconstructed SWE datasets through a simple snow temperature index model. These reconstructed datasets therefore have "standardized" snow physics. We identify and correct for relative biases in the forcing data, resulting in 50% reductions in SWE bias, indicating the propagation of forcing biases into SWE biases. However, through several SWE metrics at the continental scale (e.g. mean SWE, max SWE), we find strong correlations in the range 0.84 to 0.96 between all the reconstructed datasets. This is not observed between the native SWE products, which have correlations below 0.4, suggesting that snow model and data assimilation differences affect the interannual variability of a given product more than relative forcing biases do. We conclude that comparison to a temperature index model helps diagnose some inconsistencies between snow products and helps assess the impact of changes in data assimilation schemes and input data.