Hi,
Have skiied the last 5 years in Korea late Jan/early Feb (chinese new year) - at Muju and Yongpyeong - both are adequate resorts with enough skiiing for a week for an intermediate/advanced - though not enough for the experts. Apparently these are the two top resorts in Korea.
My favourite was Yongpyeong, better range of slopes and fewer snowboarders - hotel Dragon Valley is old and a bit shabby, but right on the slopes. You can get hostel/apartments - but difficult to work out how to book them online
Muju - better hotel (again right on the slopes) but very expensive for what it offers. Apartment in Muju was easier to sort out.
Both resorts have bus links from Seoul - seem to remember at Lotte World? You can find out by using the resort websites.
Both resorts have ski school - with limited English instruction - and you end up paying quite a bit for a private English ski school lesson.
Equipment and passes etc - you pick up on the day you want to ski - efficient system - lower end range of rental equipment - but passable (you can even rent a ski suit there!).
Make sure you check out what discounts for equipment rental/ski lift pass are available for wherever you are staying (they charge higher prices for people staying out of the resort).
Bring enough cash as difficult to get to an ATM once in the resort - they do take credit cards for paying for hotels/passes/equipment.
Night skiing on offer at both resorts - no off piste available. Neither resort was crowded (by European standards) at any time - however the peak holiday days of Chinese New Year did mean there was a short lift line at the bottom of the valley.
Both resorts will have snow at this time of year - the better snow being at Yongpyeong - much of the snow at Muju is supplemented by artificial snow. Snow starts melting in Muju in early March (we did a quick trip one year in March and it was only just skiiable)
We flew in and out of Seoul and usually spent one night in Seoul either at the end or beginning of our trips depending on flight times and bus connections to resort. Roads were clear to both resorts every time but we did travel once on the peak travel day for the Chinese New Year and that doubled the journey time! We have also hired a car to get us to resort and that was easy - even with no Korean - we just followed the sat nav.
Muju offers more resort facilities like restaurants and a prettier place to wander around, Yongpyeong offers better snow and skiing, cheaper hotel (though not cheap). My preference is Yongpyeong.
Hope this helps