I am building my first coop. Was thinking about lining walls with thick cardboard to create a 1.5" deep re pourposed air pocket insulating layer. Will chickens tear that up? Better to use some sort of thin wood underlayment?
I wouldn't. It will get wet, either from waterers being sloshed around, or poop landing on it, and then it will be a bacteria trap.
You probably don't need insulation. There are chicken keepers in Alaska who don't insulate their coops and if the birds can survive there, they can probably survive about anywhere. I've never either heated or insulated a coop and I've never lost a bird to the cold. So long as there are no drafts blowing cold air on them while they roost, they will be fine.