Is the OP in a hurry to catch a morning train or already has booked & paid accomodation?
Otherwise I'd personally be much happier spending a few hours at either a transit hotel or sauna at or near ICN and only head to the city in the morning.
I've lived several years on Mt.Namsan just a walking distance from Seoul station and it would take a lot to persuade me there that early in the morning. No shops or restaurants open, nothing to do but dodge wandering homeless & alcoholics.