A bivy is a very viable tool in winter use. I question if it is smart to not use a bivy in winter, be it in a snow cave, tarp or tent.
Non-waterproof (or not 100% waterproof, keeping in mind that no material really is - except maybe a plastic bag) because the more breathable material around you, the better. Indeed there's no moisture coming through the pad. The snow which might be blown to the side of the bivy & CCF pad is in my experience minimal, and does not pose a risk of wetting through - tyvek has a bit of waterproofness, which is sufficient for dealing with spindrift and drizzle.
"There are many grades of tyvek available, which do you use? I have used house wrap and it was stiff and noisy."
As I purchased my tyvek bivy from Laufbursche I can not tell you which exact tyvek was used. It is fairly light (205 gram for a 220 cm long bivy with a mesh window) and soft to the touch. Maybe you should ask him or some of the others here, which tyvek is good for this purpose. IIRC he even posted a guide here about that bivy...