You can cover them but they shouldn't be letting any snow in unless they have holes in the screen. More venting in the front is a good thing even if it only works when you aren't in deep powder.
The snow comes in through the seams on the belly pan, were the hood meets the fender, and through the hood vent holes. I would get a good quality bag like the put on the back or under the seat and then put your stuff in there inside double zip ziplock bags.
The belt holder originally set in the front right under the exhaust pipe so the heat from the pipe would keep it dry, but down in the nose it would get wet.