Is the Guinea Pig inside? Remember their natural habitat is the Andes in Peru.
I had Guinea Pigs for many years. They lived outside in a huge cage with plywood sides on the West Coast of Canada, it does freeze here in the winter, but not nearly as cold as it gets in Michigan. I would fill the cage with Alfalfa and they would snuggle down. I also put a blanket on the top and open end in really cold weather.
If the pig is inside, just give her something to burrow into, a show box works well and can be replace for free. Cut open one end. My grand father made mine a plywood house, when he built the big cage. They chewed around the edges of the plywood, but that did not cause any harm.
Guineas are chewers and I would not put anything in the cage that was not digestible.