I have never had any issues shooting on pow days while it is snowing. I do make sure to wipe all the snow that does accumulate when I have my camera out, but the weather sealing is pretty good so I have never had any issues. Always good to keep a couple spare dry cloths to wipe stuff down too. Then at the end of the day, I will take all my camera equipment out of my bag and let it air dry.
Make sure your bag is fully closed like mentioned above. It's real shitty when someone throws a slash or spray towards you and your bag fills up. That was definitely a one time mistake when I first started shooting because I was in a rush. Just take your time.