I want to visit Shimla when it snows. When is the right month for me? Priority is on Christmas.

I would say if you want to visit Shimla when it snow the right month for you would be December to March which is the ideal time for snowfall. And if your priority is on Christmas you must plan during that time because you might get a chance to see snowfall.

And if it is possible you can also add Manali in your itinerary because if you want to see snow then Manali is the places for you where you can find tonnes of snow and if you get lucky you might get a chance to experience live snowfall as well.