Screened bottom board going into winter — slide the tray in or leave the mesh open? Give me your regional answer

Fourth year in Hokkaido, five hives. Our winters are serious: minus 15 to minus 20°C, a metre of snow by January, hives buried to the roof most of February. I switched all five to screened bottom boards with removable trays this spring, mainly for mite drop monitoring, and now I'm facing the first winter with them. Every UK book and forum I read says leave the mesh open all winter, the bees are fine, and the damp matters more than the cold. Every local beekeeper I ask says close everything and insulate. I've got 5 cm of foam over the crown board and a small upper entrance that I keep clear of snow. I suspect the honest answer is "depends where you are", so I'd rather hear it that way: what do you do with the tray, in what climate, and why?