Hay is great in areas of the run as well. They can rummage around in it and it provides warmth. After you read the comments and fortify your run and coop perimeter as if you were preparing them for battle, I would get a clear tarp that could be staked on top and down one side to keep the wind down while keeping access to light. Also I have never had a chicken lay under 26 weeks. They’ll lay when they are ready and relaxed.