I have been to New Orleans many, many times, and my memory is that it does not get that cold. My experiences have been somewhere in the low to mid 60s, although I recall the humidity was always high.

OP being from Chicago will appreciate the warmer temperature around New Years vs. Chicago, for sure. As a resident of Southern California, I have never, ever experienced "frigid cold" in New Orleans in my many, many visits as someone else had many, many years ago. IMO, the frigid cold was more an anomaly rather than the expected. Simply, I suggest bring a light jacket or windbreaker, and you will be fine.

If OP stays near French Quarter, or even Convention Center area, then walking could be the primary mode of transportation, at least that was what I usually did when I visited.

As a visitor, I would suggest staying and visiting the French Quarter. There are lots to do and see--From sitting and enjoying sipping coffe or hot chocolate and people watch at Cafe du Monde, to taking a river cruise tour, to simply walking the many streets with shops, including Bourbon Street, to enjoying the many, many restaurants in the area.

I am not a drinker at all, yet I have always enjoyed my time visiting New Orleans.

Enjoy your trip.