Threads like this one lead to broad generalities about "3 season" v. winter, etc.

I saw a documentary called "Christmas in Yellowstone" on PBS. Part of it was about a photographer who was skiing around and taking pictures. He used a tarp and did so during a storm. However, I could see that he was sleeping in a Western Mountaineering Bag-I saw the label in a close-up. My guess is it may have been a Puma or Bison from the size of the bag-these are $7-800 bags.
http://www.pbs.org/wnet/nature/yellowstone/survival.html

So, the point is, sure you can get away with a tarp in winter, as long as you have the best bag money can buy.

Remember, people have paddled, rowed and sailed tiny boats across the oceans, but that doesn't mean it is a good idea.