several of my hives don't have any bottom board at all. the lowest box is just open to the air on the bottom. anything that might otherwise clutter up a bottom board or start molding or try to climb back aboard a bee to cause problems just falls to the ground instead. most folks would probably recommend against this option. there's a pretty good chance that bees will consume more honey keeping warm over the winter without a bottom board. there's also a chance that a hive will be more vulnerable to predation and robbing without a bottom board because they've got a lot more territory to guard. but there's also a chance that the colony will adapt to the situation and more bees will act as guards and end up less vulnerable to predation and robbing than with a bottom board at some small-ish metabolic cost to the colony because those guards won't be foraging or doing any of the other important tasks bees do. I do recommend trying this if you've got more than one hive and you're willing to experiment a little (or if you're stingy). if you do choose this route, it's probably worth sheltering the hive from wind as well as you can.
-$10 (subtract $10)