My first winter with wire boxes, but last winter I had four rabbits that did not use their nest boxes, and made a hay nest on the wire, and keep their whole litters alive, though single digit temperatures. They would cover up the top of the litter, with hay too.
I had one rabbit deliver during a single digit temperature night, found them when I checked the next day, warm and well fed. I normally give a full flake of coastal Bermuda hay, and allow the rabbit to decide how to use it, and I have been lucky in that the does have the nest boxes densely packed, too.
What I have noticed, about those nests, is that the rabbits pack the hay densely. I was curious as to how densely, and I have been able to lift out a whole nest (after the babies left it), and it was almost like it was woven, and lifted out in one piece.
I have managed to do almost the same thing, when I had to move a litter (from one wooden nest box to another), by packing in the maximum amount of hay that I could, then slowly hollowing about an small, semi deep area to put the fur and babies in, then gave it a roof of hay.
There is a downside with doing this, there ends up being a lot of hay under the cage, at first. I have been taking that hay (before it gets too many rabbit pellets), and putting it in the chicken coop, for the chickens to scratch around in.
Will be seeing if the same holds true, about the rabbits packing the hay in, for wire nest boxes this winter.
Best of luck.
Both these litters were born 3 days ago, on the 19th, and night time temps have been around 40F. I tried to get a good photo, of where it looks woven, right behind the Dutch's blue food bowl, but...
The red mini Rex, has the nest box, that I was referring to, that had to be packed.
I added some images, to my album, here
gallery/album.php?album_id=137