Most of the tarps that are used for hammocking (winter or 3 season) are made of silnylon or cuben fiber. Both waterproof and non breathable fabrics. So enclose your hammock with doors on the ends and close to the ground greatly reduces breathability and causes a large amount of frost to accumulate on the interior of the tarp.
Generally speaking hammock people tend to be in the lightweight to ultra-light weight category. So their gear choices are made with that fact in mind. In winter, I choose to use a hybrid approach with my canvas wedge hot tent that I string my hammock through. I use modern insulations and clothing. My overall method of gear selection, is function first with other factors being secondary (cost, materials, weight, packability, etc).
At the end of the day, getting out in the woods in any season, is most important. How you choose to do that gear wise, is a matter of personal preference.