Just take the filter off the cage and run the cage with the screen only. I've been doing this all year. Blower pow the gets in the box will suck right through the screen and it won't plug up or restrict hp. Wet snow doesn't even get into the airbox at all. I also put some duct tape over the side vents.
Don't worry about some snow going into the engine. People always try to tell you it will ruin something but I've been sucking buckets full of snow every season for the last decade with no failures of any kind. The only thing it will do is slowly errode the leading edge of a turbo vane but even then my turbos worked fine for many seasons. Power is the name of the game and anything that blocks all the snow will cost you horsepower and air flow.
Just make sure you run it long enough to dry the internals of the engine. That doesn't take long on a 4 stroke, a mile road ride back to the truck is plenty.
