We have screened bottom boards in both hives. In the Tardis [in the front] we put solid inserts for the winter because it's a horizontal hive, but in the flower lang [in the back of the photo], we left the screen open for the winter. In addition, I put pencil ends in each corner of their telescoping [top] lids to keep the lids propped up a bit so that air can move across the inner covers and evaporate the moisture that builds up inside.
Moisture is bad. The inside of the hives will stay warmer than the outside, so the moisture from bee breath and honey will condense. Then if it really gets cold, that condensation will freeze everywhere in the hive and kill a lot of them. The object of the winter game for beekeepers is to keep them dry. They'll handle the cold on their own.
This pic was taken after the first little snow. We've had another 16 inches since. You'll see that their front porches are covered in snow. After the pic, I cleaned the snow from in front of their lower entrances and made sure the top lids were pushed [and therefore open] to the front. That allows air in and out.