I remember a few years back a snow board accessory company put out a pole thing that you could use like ski stocks to push on the flat, but due to the standing position I don't believe it worked very well. You could potentially use something like that.
Not sure I waoul want to use a good carbon paddle on the snow. Snow is far more abrasive than it looks, I doubt it would be very good for the paddle.
totally non functional, the paddle is supposed to assist turning, looks like they are struggling to turn with it??? doing a regular on edge turn at speed without a paddle would have you twice as close to the ground and the board riding mostly on rail, enabling you generate speed out of the turn using the flex of the board, the paddle would actually slow you down. might help if you were riding a 10' snowboard??? hey thats an idea!!!! ha ha ha