Here’s a 6-minute video that shows what happened to one of my hives that was completely buried in snow for a week or two — and by completely I mean all the entrances were blocked too.
The bees couldn’t get out for cleansing flights and made a big stinking mess of the hive, or at least their hive entrance. The 6mm / quarter-inch mesh I use to keep shrews out probably made the mess even worse. Who knows, maybe the heat from the colony would have melted the snow around the top entrance and allowed the bees to get out just far enough to poop. Maybe. But for now, especially if my area ever gets hit with an insane snow storm again, I may have to put 12mm / half-inch mesh around the entrances and hope for the best.