Planning in unstructured environments is challenging -- it relies on sensing, perception, scene reconstruction, and reasoning about various uncertainties. We propose DeepSemanticHPPC, a novel uncertainty-aware hypothesis-based planner for unstructured environments. Our algorithmic pipeline consists of: a deep Bayesian neural network which segments surfaces with uncertainty estimates; a flexible point cloud scene representation; a next-best-view planner which minimizes the uncertainty of scene semantics using sparse visual measurements; and a hypothesis-based path planner that proposes multiple kinematically feasible paths with evolving safety confidences given next-best-view measurements. Our pipeline iteratively decreases semantic uncertainty along planned paths, filtering out unsafe paths with high confidence. We show that our framework plans safe paths in real-world environments where existing path planners typically fail.