The unprecedented growth of mobile video traffic is adding significant pressure to the energy drain at both the network and the end user. Energy efficient video transmission techniques are thus imperative to cope with the challenge of satisfying user demand at sustainable costs. In this paper, we investigate how predicted user rates can be exploited for energy efficient video streaming with the popular HTTP-based Adaptive Streaming (AS) protocols (e.g. DASH). To this end, we develop an energy-efficient Predictive Green Streaming (PGS) optimization framework that leverages predictions of wireless data rates to achieve the following objectives 1) minimize the required transmission airtime without causing streaming interruptions, 2) minimize total downlink Base Station (BS) power consumption for cases where BSs can be switched off in deep sleep, and 3) enable a trade-off between AS quality and energy consumption. Our framework is first formulated as a Mixed Integer Linear Program (MILP) where decisions on multi-user rate allocation, video segment quality, and BS transmit power are jointly optimized. Then, to provide an online solution, we present a polynomial-time heuristic algorithm that decouples the PGS problem into multiple stages. We provide a performance analysis of the proposed methods by simulations, and numerical results demonstrate that the PGS framework yields significant energy savings.