I've been to Nanjing a few times, first time when China Eastern still flew direct from Singapore (went during golden week so crowds in Singapore seems like a walk in the park to me), and later on via High Speed Rail from Shanghai when they stopped that route.
Never been there during winter so can't comment on the weather but it should be cold enough. It's a historical city so do go see the historical sites including the museums. If you're not into historical stuff, you'll get very bored (I was still okay hehe). Unfortunately I can't read chinese but it's still worth looking at.
Nanjing Massacre Memorial
Presidential Palace
Sun Yat-sen Mausoleum (don't forget to look up to see the flag when you're at the statue)
Ming Dynasty Mausoleum
Xuanwu Lake
Nanjing City Wall - One of the most complete city walls still standing.
Fu Zhi Miao
Sun Yat-sen and Ming Dynasty Mausoleum are situated near Purple Mountain.
These are the ones I can remember, I've been to all except Ming Dynasty Mausoleum
The signature dish there is Salt water duck, Yen shui ya. Of course there are other stuff as well. The roasted duck is good too if I remember correctly.
Haven't been there in a while, maybe should make a trip back to see my friends.
If you're arriving at Lukou airport, there is now a subway station there to head to the city. How convenient! Last time I had to take a limousine bus to the Nanjing Railway station then transfer to subway.