I went on a short work trip to Seoul just last week and managed to visit quite a number of the popular tourist destinations over the weekend. The temperature was around the range of -12 to 5 °C and I was pretty happy with my down jacket with warm pockets from Uniqlo.
This was my first experience with winter and I guess it's sufficient to go with at least a long-sleeve fleece t-shirt and a good jacket for top. Sometimes, I layer on a wool cardigan between my fleece shirt and jacket. When it gets cold, I put on the hood to protect my ears (ears do feel the pain from the cold) and use a scarf to cover my mouth/nose. For bottoms, jeans was enough for me but I wore a heat-tech tights from Uniqlo to protect my thighs from abrasion due to too much rubbing against the cold and stiff jeans while walking alot.
I also got a prepaid SIM card with mobile internet, but came to the conclusion that it is actually quite troublesome and expensive to use it. So, my recommendation is that you stick to your roaming phone with data roaming if you really need internet desperately. Prepaid SIM is probably more worth it if you are staying in South Korea for at least 2 weeks. It's definitely not worth it if you are around for only 1 week due to the expensive starter package (₩8800 for SIM, ₩30,000 minium topup and additional amount for internet plan, e.g. ₩5500 for 100MB usage).
During my 1 week stay, I found that the language barrier was very challenging and was unlike all the other cities I have ever visited before. Firstly, most Koreans speak very limited English. Secondly, most of the eateries/restaurants outside the tourist spots only have Korean menus and very limited or no pictures. Sometimes, I had to settle for fast food or dine in a chinese restaurant which has menu written in chinese as well.
As for public transport using the metro, it was quite manageable most of the time. The English brochure with the system map and travel highlights wasn't that commonly available though. I suspect they are only found in certain popular metro stations in city centre. One point to pay extra attention to is when certain metro lines branch out to 2 "sub-lines". That's where you have to listen very carefully to the announcement where the next train is headed to. I took the wrong train once and had to exit at a station, pay for a new ticket, enter and take the right train to my destination. In the metro stations, there are indications of the names of the next/previous station at the platforms. In the train, there is also announcement (in Korean) and a screen display of the name of the station the train is approaching.
I guess these kinda sum up my brief experience in Seoul. I shall create another post to highlight on the places I visited.