This paper presents an adaptive energy-aware prediction and planning framework for vehicles navigating over terrains with varying and unknown properties. A novel feature of the method is the use of a deep meta-learning framework to learn a prior energy model, which can efficiently adapt to the local terrain conditions based on small quantities of exteroceptive and proprioceptive data. A meta-adaptive heuristic function is also proposed for the integration of the energy model into an A* path planner. The performance of the proposed approach is assessed in a 3D-body dynamic simulator over several typologies of deformable terrains, and compared with alternative machine learning solutions. We provide evidence of the advantages of the proposed method to adapt to unforeseen terrain conditions, thereby yielding more informed estimations and energy-efficient paths, when navigating on unknown terrains.<div>Submitted for revision to IEEE Transaction on Cybernetics.</div>