The bay is interesting in normal times, too, as it's an extension of the Arctic Ocean into the middle of Canada that kind of refrigerates the climate there through feedbacks between the ocean, atmosphere, and continental landmass. The default latitudinal boundaries between earth's polar and temperate seas are 60 degrees N and 60 degrees S, but the usual climate of Hudson Bay gets it it included as part of the Arctic Ocean despite its lower latitude. Conversely there are parts of the North Atlantic above 60 degrees N that are warmed by the Gulf Stream and not considered part of the Arctic Ocean. Watching how anthropogenic climate change is shaking up the usual climate / ocean boundaries is interesting but also scary because of the rapid environmental and geopolitical change it's causing. One interesting tool that US has (for now) for viewing polar conditions is the National Snow and Ice Data Center's "sea ice today" website. https://nsidc.org/sea-ice-today Highly recommended.
