This is really quite simple (depending on difficulty), but the most important thing to remember is to make camp somewhere where you are protected from the wind, so that your campfire won't die out. Gather enough lumber and food, and you have food, water from snow, and warmth and safety from the fire.
15 sticks and 5 cloth will let you create a snow shelter from the campcraft menu, this helps a lot against cold, but you still need to camp out of the wind. If the wind turns, just move camp.
Another good tip is to bring coffee (or tea, if you don't have coffee). This will warm you up and reduce your fatigue.
Also: You don't need to camp far out in the wilderness; just outside your home base is just fine, in case you're worried that things might get rough.