Navigating autonomous robots through dense forests and rugged terrains is especially daunting when exteroceptive sensors -- such as cameras and LiDAR sensors -- fail under occlusions, low-light conditions, or sensor noise. We present Blind-Wayfarer, a probing-driven navigation framework inspired by maze-solving algorithms that relies primarily on a compass to robustly traverse complex, unstructured environments. In 1,000 simulated forest experiments, Blind-Wayfarer achieved a 99.7% success rate. In real-world tests in two distinct scenarios -- with rover platforms of different sizes -- our approach successfully escaped forest entrapments in all 20 trials. Remarkably, our framework also enabled a robot to escape a dense woodland, traveling from 45 m inside the forest to a paved pathway at its edge. These findings highlight the potential of probing-based methods for reliable navigation in challenging perception-degraded field conditions. Videos and code are available on our website https://sites.google.com/view/blind-wayfarer