It's nice to have a bone dry pair to sleep in. One pair a day is more than enough to me. By changing briefs you keep your long underwear or in my case, my bike tights, cleaner on multi-day trips. It would be absurd to carry an extra pair of polypropylene long underpants for cleanliness. Skimpy nylon or silk ones are not bulky at all and dry fast.
Cotton is ludicrous.
If you're out for a week you may want a few pairs. This way you can stay dry and as cool as possible when hiking up while it's snowing and it's not so bulky to stash. It's got to have a good hood that can be cinched down with mittens on. Pockets to hold maps and snacks are real convenient so you don't have to take off your pack so much. A powder waist helps keep in warmth and snow out without restricting leg motion.