Autonomous Unmanned Aerial Vehicles (UAVs) must reliably detect thin obstacles such as wires, poles, and branches to navigate safely in real-world environments. These structures remain difficult to perceive because they occupy few pixels, often exhibit weak visual contrast, and are strongly affected by class imbalance. Existing segmentation methods primarily target coarser obstacles and do not fully exploit the complementary multimodal cues needed for thin-structure perception. We present EDFNet, a modular early-fusion segmentation framework that integrates RGB, depth, and edge information for thin-obstacle perception in cluttered aerial scenes. We evaluate EDFNet on the Drone Depth and Obstacle Segmentation (DDOS) dataset across sixteen modality-backbone configurations using U-Net and DeepLabV3 in pretrained and non-pretrained settings. The results show that early RGB-Depth-Edge fusion provides a competitive and well-balanced baseline, with the most consistent gains appearing in boundary-sensitive and recall-oriented metrics. The pretrained RGBDE U-Net achieves the best overall performance, with the highest Thin-Structure Evaluation Score (0.244), mean IoU (0.219), and boundary IoU (0.234), while maintaining competitive runtime performance (19.62 FPS) on our evaluation hardware. However, performance on the rarest ultra-thin categories remains low across all models, indicating that reliable ultra-thin segmentation is still an open challenge. Overall, these findings position early RGB-Depth-Edge fusion as a practical and modular baseline for thin-obstacle segmentation in UAV navigation.