Hi Cold
Oct is actually autumn, temperature wise is like being in an aircon room but with sunshine above you. Its not that cold compare to Korea's Winter. Pple in Korea are reasonably well-dressed especially the ladies. It's normal to see men walking around in suits too. So it's okay for you to wrap yourself up with clothes when you are there.
A bit tough if you ask me where is romantic...I merely walk ard on my own cos I was on a free and easy trip with my husband. I went to a number of places using their subway. It was fun. Their subway network is far more advanced than Singapore's. You may wish to go to Mount Sorak - heard it is nice. I did not go cos it takes 5 hrs to travel there from Seoul.
As mine was free and easy, I bought the air ticket from a travel agent and book my accomodation thru the net. You can get travel info from the KNTO (Korea National Travel Organisation. There are KNTO branches at major tourist spots such as Dongdaemun, Nandaemun, Cityhall Subway Station, Jong-gu. The staff are friendly and best of all, they speak English. Most koreans do not understand English including some hotel receptionists!
BTW, KNTO has a branch in Singapore too...at Clifford Centre.