I think you want to do all of the great things you can do in Paris at any time of the year!
But, given that it will be cold, there is also plenty of time steal away for some sweets indoors... I would recommend doing tea at Mariage Freres in the Marais (rue du bourg-tibourg), coffee and macarons at Laduree on the Champs Elysees, and a trip to Angelina on rue de rivoli for their delectable chocolat chaud. But maybe not all in the same day!
There's also great shopping at Le Bon Marche on the left bank, and Galeries Lafayette and Printemps on the right bank.
Finally, if you like to ice skate, there's seasonal skating at the Hotel de Ville.