Heurigers open in December?

Many of them are open, but the seating will be inside. Normally visiting Grinzing is to go up and have a meal and back to Vienna. In the winter, you probably won't even want to walk in the vineyards and woods, so a day there would not be a wise use of your time (any time of the year in my view ;-) ) . Maybe if the skies are clear and you go up for the view and want to eat on the way back to the city, it would make sense.

FWIW, my favorite is Hengl Haselbrunner. They are open in December except Christmas eve and Christmas Day.
http://www.hengl-haselbrunner.at/
The food is very good, as is the wine (no such guarantee in Grinzing) , no tourists/tour groups, accessible by public transport. Good idea to get reservations as they are busy in summer and do a fair number of parties in winter but a couple days ahead should be fine. They don't have a view of the city (nice garden), but in winter, you will be sitting inside anyways.

Enjoy! I hope you get snow for your visit!

Yes, as mentioned above, the heurigen experience is greatly diminished in the winter as the joy of a heuriger is sitting outside under the chesnut trees in the summer or warm fall. This visit will likely have been preceded by a walk through the vineyards.

In addition, and as hinted above, Grinzing is not really the best heurigen area as it is full of tour buses and not the best food/wine. Viennese don't really go to that area. It used to be nicer before it was found. Anywho, there are many better areas, such as Perchtoldsdorf, Stammerdorf, Neustift am Walde and Nussdorf. Is it a good idea in December, not really.

We stayed in Perchtoldsdorf for a month in August 2 years ago. We went to a heuringer almost every evening trying out several of the more than 50 that were in this small town. While I agree with the 2 previous posters I must say that some of our town's heuringer had wonderful intimate indoor seating with little fireplaces and antique decor. I can only image that in the month of December they would be decorated with Christmas finery. To my knowledge none of our local heuringer had views of Vienna yet they managed to be warm and inviting. The best part, however, was sitting outdoors under the grape vines sipping wine, eating simple food and listening to the joyful conversations of neighbors and families.

I'm not recommending that you get yourselves to Perchtoldsdorf though because the nearest train station is a mile or two away but if you can find a concentration of them in the area the previous 2 posters are recommending, I think it would be worth the experience if you have the time.

Heuringer tend to cycle through which ones are open when. Perchtoldsdorf has a 12 month calendar to let people know which ones are open for a 3-4 week period of a time. They also have these metal signs at the beginning of towns/neighborhoods to let you know who's open at the time.

We found that it was also necessary (for us) to stand back and watch for a couple of minutes to see what was the sequence of ordering protocol. It helped us not hold up the line. In the month we were in our town, we only heard English spoken at a heuringer 2-3 other times so we needed to observe the locals then we just jumped right in. Loved our experience. Hope you can find an intimate, local evening at an authentic heuringer too!

EDIT: if you aren't able to go to a heuriger while you are in Vienna, look for a white local varietal on the menus in the city, a Grüner Veltliner.

Regarding the possibility of a winter walk in the Vienna Woods: On 24 January 1993 - and I recall this exact date because it was one week after the birth of my daughter - a friend and I took a walk in the Wienerwald on what turned out to be a beautiful, blue sky sunny and quite warm day. In fact, at 63 degrees F, it was the warmest day of the year vs. the average temperature for that date (see historical weather data). Our walk ended with a nice (indoor) heuriger meal. I recall that the winter weather returned a few days later.