hi.
december in seoul is quite cold. brrr...
i am from korea and that's part of reason why i am in singapore now
as everyone suggested, it would be better to get winter clothes there.
dongdaemoon market is good. it's open basically all day & nite
- retail during day, wholesale at nite.
but it's crazy place and you would have to bargain, bargain.
another place you could try is 'express bus terminal' subway stop underground arcade.
it's a long long stretch of small shops(almost long as orchard road)
and you can find good bargains there.
at the far end of stretch, there are few shops that sells US labels like 'gap' 'abercrombie&fitch' for $1, $3 or $5. think they are factory over-runs and slight irregulars but quite good. just have to dig thru piles of clothes among so many fiesty aunties... pure exercise.
best bet is to buy pait of long-johns you can wear inside rather than getting bulki coat you will never wear again. Cold weather in Korea is not feeling cold outside of your body but rather it creeps inside your body... strange it might seems.
have good time in korea and let me know if you need any help on where you want to visit aside from touristy area. there are many places in seoul that are not just concretes and shopping!