In this paper, we focus on reducing the on-grid energy consumption in heterogeneous radio access networks (HetNets) supplied with hybrid power sources (grid and renewables). The energy efficiency problem is analyzed over both short- and long-timescales by means of reactive and proactive management strategies. For short-timescale case, a renewable-energy (RE) aware user equipment-base station association is proposed and analyzed for the cases when no storage infrastructure is available. For long-timescale case, a traffic flow method is proposed for load balancing in RE base stations (BSs), which is combined with a model predictive controller (MPC) to include forecast capabilities of the RE source behavior in order to better exploit a Green HetNet with storage support. The mechanisms are evaluated with data of solar measurements from the region of Valle de Aburrá, Medellín, Colombia and wind estimations from the Moscow region, Russian Federation. Results show how the green association proposal can reduce on-grid energy consumption in a HetNet by up to 34%, while is able to exceed the savings obtained by other methods, including the best-signal level policy by up to 15%, additionally providing high network efficiency and low computational complexity. For the long-timescale case, MPC attainable savings can be up to 22% with respect to the on-grid only Macro-BS approach. Finally, an analysis of our proposals in a common scenario is included, which highlights the relevance of storage management, although emphasizing the importance of combining reactive and proactive methods in a common framework to exploit the best of each approach.