I would personally spend as much time as i possibly could in Copenhagen. Love the place ^

I actually think its best when its cold out and the nights are drawing in. You can do the main sights in daylight and find a cosy pub to wait for your onward flight in. The train takes about half an hour from memory but the station is a little way from some of the major sites (The Little Mermaid is on the other side of town for example).