In this paper, we introduce a novel algorithm for incorporating uncertainty into lookahead planning. Our algorithm searches through connected graphs with uncertain edge costs represented by known probability distributions. As a robot moves through the graph, the true edge costs of adjacent edges are revealed to the planner prior to traversal. This locally revealed information allows the planner to improve performance by predicting the benefit of edge costs revealed in the future and updating the plan accordingly in an online manner. Our proposed algorithm, risk-aware graph search (RAGS), selects paths with high probability of yielding low costs based on the probability distributions of individual edge traversal costs. We analyze RAGS for its correctness and computational complexity and provide a bounding strategy to reduce its complexity. We then present results in an example search domain and report improved performance compared with traditional heuristic search techniques. Lastly, we implement the algorithm in both simulated missions and field trials using satellite imagery to demonstrate the benefits of risk-aware planning through uncertain terrain for low-flying unmanned aerial vehicles.