In January, the alligators are hibernating so, while the swamps tours are still running, you will probably not see an alligator. But the trip is still worth your money in that you are in the swamps!!
The trip from the French Quarter is accommodated by a driver who will pick you up at your hotel or B&B and drive you to the swamps. You have a choice of just doing the swamp tour or doubling it up with a trip to a plantation home or graveyard tour. Who wants to see a graveyard? In New Orleans, you want to tour the graveyards, which are filled with history (of course) and everyone buried there lies in above-ground tombs because New Orleans is below sea level.
The swamp tours and plantation home tours are worth your time whether it is warm or not. It's back to nature and even a little scary when you're in the middle of nowhere and at the mercy of a tour guide who knows the area like the back of his hand.
If you take these tours, you will be picked up at 8am and returned around 2pm(we got back at 3pm). If it's the off-season, take some snacks, because the tour office is at a skeleton crew and lunch or drinks aren't included.