The presence of Arctic sea ice currently limits surface ship travel in the Arctic for most of the year. However, due to rising temperatures from global climate change, Arctic waters are becoming increasingly navigable for a greater percentage of the year. As interest in surface travel within the Arctic increases in the coming years, the safety of a ship operating in this context must be considered. Specifically, the possibility of ice accumulation on the topside of a ship is heightened due to environmental factors within the Arctic, including the presence of sleet, snow, freezing rain, and freezing spray. This additional mass on exposed topside surfaces, at the most extreme, could result in capsizing of a vessel. The present research develops a framework to monitor evolving mass properties for a ship in Arctic operation, in order to ensure safe travel through the Arctic. As with any real-world application, the data for this work are limited and noisy, and the system is complex. When the real-world data are limited, when the signals of interest are noisy, or when mechanistic models are unavailable, stochastic inference can enable informed decision making regarding the natural and built worlds. Thus, this work leverages stochastic inference in order to investigate the real-world problem of Arctic travel. First, the dissertation presents a proof-of-concept for applying this framework to identify a single mass parameter for the Research Vessel (R/V) Melville with no icing and in quiescent seas, both at model-scale and full-scale. Second, the framework is extended to consider multiple mass parameters of the R/V Melville while undergoing potential ice build-up configurations. The third component of the dissertation looks outwards to the sea, to gauge the near-field wave forcing acting on the ship. In particular, the present work reports on a validation experiment of an existing algorithm to determine scale and sea state from an uncalibrated camera. Taken together, the chapters prepare a foundation from which an ice monitoring system could be implemented. The chapters also provide insight to the specific challenges that exist for the full realization of the proposed framework. While the presence of ice is a focus of this work, the framework could easily be translated to a ship operating in within a context in which any mass property is evolving; those systems may require the monitoring of different mass parameters, but the underlying framework and approach proposed here would remain unchanged.