I have a large wooden crate in their pen for cover. I moved some bedding today and it was not frozen. I have blocked off wind from the north and west, so that helps. The plywood should help, but when it rains and then freezes, these may be no good way to keep the bedding from freezing. You might just add more dry bedding over the frozen stuff. Yes, it makes a bigger block of frozen stuff when it rains again if the plywood doesn't help, but it might help for a bit anyway. There really is no good way to protect the bedding in a chicken wire pen. My ducks didn't seem to mind this spring when I first got them if the bedding froze or not. (It did freeze a couple of times overnight as it was very cold in March.) Oh, I have also used a vinyl flap over the front of the crate to help keep out rain—rain it part way down. If it's getting up high enough in temp that it can rain, they may be fine. Good luck with this—it's really pain.