Aside from Hotels and 여관s, many smaller villages (especially those around Parks) have minbak, 민박, more basic rooms for rent. Campgrounds are getting more popular, and while the amenities often close in winter, you can still camp. Many mountain huts, 산장, are open year round, especially those on popular winter trails. Call ahead or e-mail (info on National Park home pages). A bunk costs $5 and sometimes comes with mat/blanket. Basic Korean food, snacks and water are usually for sale. On winter trips, another great alternative are 찜질방, coed 24-hour saunas. They are found in most cities, and unlike 24 hour saunas, they provide shorts and T-shirts and a large co-ed area of saunas, video-games, PC-bang, no-rae bang, TV rooms, restaurant, snack bars, etc. . . the men's and women's bathhouse areas are still separate. There are often cubbie-holes you can stake out if you come early for a little privacy. Ear-plugs can come in handy, though many have quiet sleeping rooms. Once you're in, you're in, but they'll let you stash your pack, walk around the city, and come back when you're ready. Prices run $6-10 (I still find occassional 24-hour saunas with no co-ed areas, for $5-6, in smaller cities and more rural areas.)
"If you can't do something well, you might as well learn to enjoy doing it poorly."
-- from a de-motivational poster, but I find it oddly liberating