Hiking in Soraksan is awesome in the winter! That's when I usually join the Sokcho crowd anyway...there's a great ice/winter festival every year, and hordes of people make their way up and down Daecheonbong, fueled with plenty of soju and ramen...it's really social and fun, and if there's enough snow, you can slide a good portion of the way down the mountain on your butt...don't know how much snow there is this year though, look out for rocks!
There are also plenty of other places to hike, just make sure you're dressed properly, know where you're going and have lots of food (a hot thermos is also a necessity in my books!). Also, the trails can get pretty icy, it's a really good idea to throw down your 5,000 won on a pair of eisen/eizen (I have no idea how to spell that word, you know the little mini-crampons though?) for safety.
And there are lots of minbaks...maybe check out the accommodations thread for some good places to go. Good luck!