Blood is a critical resource in healthcare and its perishable nature and variable demand challenges the blood supply chain efficiency. To aid the management of blood products and collection initiatives, time series forecasting methods can be applied to predict the volume of blood donations and needs. However, existing solutions generally neglect the role of context data sources for guiding the learning and emerging neural processing principles. This study aims at developing multi-input deep neural network models for predicting blood collections and demand that tap into the value contained in both historical and prospective sources of context, proposing dedicated context-aware neural architectures sensitive to endogenous and exogenous features (e.g., campaigns, emergencies, weather, mobility). In addition, we assess the role of additional principles, including the decomposition of series by demographic and haematological profile, as well as the exploration of architectural variants and temporal feature encodings. The acquired results from nation-wide blood data in the Portuguese territory reveal that the proposed principles, particularly the incorporation of historical and prospective context sources, lead to statistically significant improvements in forecasting performance.