Rabbit people?

Anyone have pet bunnies? My daughter's friend has a pet rabbit. Her mother lets her keep it on the porch only where there is no real protection from wind in an open wire cage. Yesterday - because I knew the temps were dropping - I made it a little wooden bunny house. He loved it. But I am thinking it needs some hay in there for bedding? Is newspaper safe? Or do I need to go get straw? Would it eat straw? Or use it for bedding?

Ages ago - ha - when I was little, my indoor bunny had stuffing that I'd used for my toe shoes in his box and newspaper outside of the box in the pen....