Accurate monthly forecasts of snow water equivalent (SWE) can be critically valuable for water resources managers to plan ahead. It is uncertain how much of the information content in satellite-based snow cover fraction (SCF) or in-situ measurements of SWE can help to improve forecast quality at a monthly lead time. Past studies of SWE monthly forecasts mainly employed data assimilation with hydrologic models, but it is unclear if the available information is optimally used. Here we apply a long short-term memory (LSTM) network with data integration (DI, referring to absorbing recent observations as inputs into deep networks) to assimilate 30-day prior observations of either SWE or SCF for SWE forecast. SWE was much more helpful than SCF, but the latter was also valuable. SWE dramatically elevated monthly forecast accuracy in terms of both root-mean-squared-error (RMSE) and peak snow, suggesting a major issue with SWE prediction was the accumulative forcing errors, rather than spatial heterogeneity. The 30-day ahead forecast RMSE is reduced from 57.8 mm with no data assimilation to 27.5 mm and 54.8 mm with SWE and SCF, respectively, and the Nash Sutcliffe model efficiency coefficients were 0.88, 0.97, and 0.89, respectively, which are higher than previous reports. Both models migrate well to untrained sites, without experiencing significant declines. Meanwhile, the difference between 7-day and 30-day data is not significant, highlighting the long-term nature of SWE model errors.