Same as in ordinary camping with tent in winter or summer
You will develop black belt in wild land defecation.
Learn how to poo immediately when you wake up. Then you can do it in the dark, just next to the road without have to walk in deep snow. Prepare a place to take a dump in the night before. Dig a hole in the snow and enjoy the moment. Keep it simple. If you want the premium version you can dig out a complete toilet and put a smal piece of polystyrene or similar to make it comfortable. Think I have a picture somewhere if you want to se it. Look for a plowed snow for best support/strength, not a pile of snow from a snow thrower or the toilet will collapse underneath you (!). If you are not in a really remote area, then put a plastic bag in the hole and hide it, but don’t forget to bring it with you when you leave the area.
Good luck