EDIT: 6th Jan 2017: Personal experience:
I was at Agra at the end of December, and although there was thick fog till 11am (visibility 50m), almost all of the fog cleared off by 13:00hrs. The pic I took below, was taken at around 13:50hrs. So even if you visit the Taj in winter, you have no need to worry about the fog.
Do note that it is better to reach the Taj early. The queues can be extremely long for Indians. I stood in one queue for 20 minutes to get the entry tickets. Another queue to get the electric vehicle to the entry gates (could've just walked). A 30 minute wait in another queue to enter the complex. An extremely long queue that starts half way from the garden surrounding the Taj, and goes all around the Taj. This was just to enter onto the elevated marble platform the Taj is on. Then there's another queue that goes around the Taj if you want to see the inside of the monument.
Tip for Indians and foreigners: If there's too much of a crowd, just take the more expensive ticket meant for tourists. You won't have to wait in any long queues. It is completely worth it. Also, (if you want a good photograph) it might help to postpone your visit until the maintenance work is completed. As you can see from the photo below, there's work ongoing on one tower. There's also work ongoing behind the Taj where they've erected similar structures.
My initial answer before 6th Jan 2017:
According to a November 2016 post about the Taj Mahal, visibility isn't all that bad; especially when you move closer to the monument. Of course, November was when smog was at its worst in Delhi, but measures have been taken to reduce it, so by the end of December it may improve.
People have shared past experiences, saying that by 10am or 11am, the fog would reduce considerably. So if you reach there too early, you could choose to visit the Agra Fort and then visit the Taj by the time the sun is up.
Some of the comments taken from users on TripAdvisor:
17 December 2013: NO need to cancel the trip...dont get
dissappointed...no doubt 16 Dec morning was very foggy buy as d day
proceed it lifted up....better to be at d Taj Mahal between 11-15
17 December 2013: In the morning weather foggy but after 11:00 am it
becomes clear. Tajmahal you can visit in evening about 16:00 pm and
rest of monuments before it.
17 December 2013: Any time of the year and in any weather - Taj is
beautifull - it is different. Moreover as sun comes out fog melts and
it is good sunlight.
19 December 2013: Its true that north india effected from dense fog at
this time. but its not effect your tour to taj mahal . Because after
10 Am its going to be low and you can drive and do every activity
which you want so keep continue and visit the world heritage site taj
mahal without think so much about fog and wheather conditions.