When to come:
Around December 10th ish the Christmas decorations go up. Its also early enough to avoid the Christmas season flight increases. 
Galleries Lafayette Christmas Tree
What to consider:
The reason Champ de Mars was virtually empty was because it was cold and raining. I was bitching the entire time. 
The best things about Paris in the winter:
Oysters
October to March is oyster season. You will see them on virtually every street corner, making oysters the Starbucks of Paris. For prime oyster spotting check out Raspail Market. This is Ina Garten's favorite Parisian market too.
Winter Clothes
Paris is the perfect excuse to bust out your most treasured winter wear. While other cities bundle up in grey's and browns, Parisians seem to do winter right with lots of prints, textures and furs. It's also a great city to experiment with fashion.
How to mix prints like a Parisian:
While there are no rules for mixing prints in Paris, us Americans feel more comfortable with some guidelines to follow so here they are: use the buddy system. Let me explain. When mixing prints, make sure each item in your outfit has at least one other complementing item. The easiest way to do this is to match colors. In my outfit below I'm mixing hound's-tooth, leopard print, and stripes. The common color being black to tie them all together. Then I took inspiration from the pop of brown in my shoes and added a brown faux fur scarf and a brown feather in my hat. And voilà!
Christmas Lights
The city of lights, does Christmas lights right. A quick and festive way to see them up close is to take an open-air night bus tour. They give you a warm beverage and classy lime green blanket to stay warm.
Greyish Skies
Gloomy grey days make for great photos. No pesky sunshine to create shadows and glare.
Sweet Treats
Ok, so this isn't specific to winter, but there's something about Christmas time that make sweet treats even more enjoyable.
And some bonus advice on how to take an outfit from chic to crazy in 5 seconds flat:
Whilst visiting London I picked up a delightful tulle skirt from Top Shop. I saw someone else pair a similar skirt with jeans and thought it looked very cool so I decided to give it a try. I was quite pleased with the result:
The problem with these risky outfits however, is you can't do anything weird without looking bat shit crazy. That is generally a problem for me. For example, you can't walk around with a huge plastic bag, picking up giant ponies:
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