We present a forecast‐based adaptive management framework for water supply reservoirs and evaluate the contribution of long‐term inflow forecasts to reservoir operations. Our framework is developed for snow‐dominated river basins that demonstrate large gaps in forecast skill between seasonal and inter‐annual time horizons. We quantify and bound the contribution of seasonal and inter‐annual forecast components to optimal, adaptive reservoir operation. The framework uses an Ensemble Streamflow Prediction (ESP) approach to generate retrospective, one‐year‐long streamflow forecasts based on the Variable Infiltration Capacity (VIC) hydrology model. We determine the optimal sequence of daily release decisions using the Model Predictive Control (MPC) optimization scheme. We then assess the forecast value by comparing system performance based on the ESP forecasts with the performances based on climatology and perfect forecasts. We distinguish among the relative contributions of the seasonal component of the forecast versus the inter‐annual component by evaluating system performance based on hybrid forecasts, which are designed to isolate the two contributions. As an illustration, we first apply the forecast‐based adaptive management framework to a specific case study, i.e., Oroville Reservoir in California, and we then modify the characteristics of the reservoir and the demand to demonstrate the transferability of the findings to other reservoir systems. Results from numerical experiments show that, on average, the overall ESP value in informing reservoir operation is 35% less than the perfect forecast value and the inter‐annual component of the ESP forecast contributes 20–60% of the total forecast value.