Recent advances in multi-modal large reasoning models (MLRMs) have shown significant ability to interpret complex visual content. While these models enable impressive reasoning capabilities, they also introduce novel and underexplored privacy risks. In this paper, we identify a novel category of privacy leakage in MLRMs: Adversaries can infer sensitive geolocation information, such as a user's home address or neighborhood, from user-generated images, including selfies captured in private settings. To formalize and evaluate these risks, we propose a three-level visual privacy risk framework that categorizes image content based on contextual sensitivity and potential for location inference. We further introduce DoxBench, a curated dataset of 500 real-world images reflecting diverse privacy scenarios. Our evaluation across 11 advanced MLRMs and MLLMs demonstrates that these models consistently outperform non-expert humans in geolocation inference and can effectively leak location-related private information. This significantly lowers the barrier for adversaries to obtain users' sensitive geolocation information. We further analyze and identify two primary factors contributing to this vulnerability: (1) MLRMs exhibit strong reasoning capabilities by leveraging visual clues in combination with their internal world knowledge; and (2) MLRMs frequently rely on privacy-related visual clues for inference without any built-in mechanisms to suppress or avoid such usage. To better understand and demonstrate real-world attack feasibility, we propose GeoMiner, a collaborative attack framework that decomposes the prediction process into two stages: clue extraction and reasoning to improve geolocation performance while introducing a novel attack perspective. Our findings highlight the urgent need to reassess inference-time privacy risks in MLRMs to better protect users' sensitive information.

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