Ok, so I recently published an article on why Paris was best in summer. I maintain that it is, but I will give you a case for Winter as well.

Some would argue that Paris is just as good in winter (or all year round for that matter) because of the holiday atmosphere.

The galleries and museums (the Louvre, the Grand Palais, the Centre Pompidou, Notre Dame Cathedral, etc.) are all indoors and are just as amazing any time of the year. They certainly don't close when it's cold!

A major plus which I actually noted in my original article is that everything is cheaper in the autumn and winter. Flights and hotels are still busy, but not as busy so you can get much better deals. Even the Ferry prices as well as some of the museum prices go down in the winter months. Getting cheap hotels in Paris certainly helps make things feel a little warmer.
You will have to note that prices are high on the 10 days before Christmas and two weeks after as people flock to the city for the holidays. Can you imagine a better place to spend New years?

Some sites such as the Notre Dame Cathedral, the Sacre Coeur basilica and Les Invalides seem more appropriate and beautiful in the winter than on a hot sunny day in my personal opinion.

I maintain that Paris is amazing to visit 365 days a year. It's time you experience it if you haven't yet.