You'll have to experiment. It's usually better to take the time to make pressure changes as soon as you think they're needed, rather than wasting energy fighting the bike on tires that are too hard or too soft. Beginning snow riders almost always run their tires too hard. As the snow gets softer, so should your tires. When in doubt, let air out.
Mini pumps offer performance similar to that of medium-sized frame pumps.
You can keep them warm inside your jacket so they work better in the cold. Presta valves are less prone to freezing up and easier to inflate and let air out of than Schraders. If your rims are drilled for Schrader valves, you can use either type of tube in an emergency. If you use conventional pedals you'll have the easiest time choosing and setting up your footwear. If you want to go clipless you'll have to devise a way to attach cleats to winter footwear or to insulate compatible riding shoes.