If you like using the side tie-outs on your BB, try to incorporate them into your sock design. My winter sock/tent has short (4") bungees that connect to my DIY hammock tieout points. Then the sock ties out to the tarp corners, and thence to the ground - saves on stakes and lines. I think keeping the side of the sock from touching the hammock helps protect from wind.
Do use a panel of fabric that breathes well overhead. If it's calendared, put the shiny smooth side in. I like the tiny tyvek footprint of my sock tent. It's easy to sweep out the snow and ice. For a sock bottom section tyvek might be pretty good. Try to include a slit at the very bottom that you can open to let the ice out in the morning.