I agree with Azerane. Bunnies like tunnel-like structures for reasons that must be genetically coded. Anything remiscent of a burrow/warren will attract them. There should be two “door-holes” because bunnies always want an emergency exit.
I live in Sweden where winters can get very cold. It’s still legal to house bunnies without extra heating (we have strict laws regarding the keeping of animals). The law states a rabbit must have an insulated hiding-space, elevated off the ground (by a foot or so, so cold doesn’t penetrate from below), shelter against rain wind and snow and direct sunshine, adequate bedding material (f ex straw), and during times of below zero Celcius degrees, be provided with fresh, warmed water twice a day (because water will freeze). In Sweden you must also provide the rabbits with a a shelf they can sit on or hide underneath. The shelf must be big enough to allow all rabbits housed together to sit together.
Does it get gradually cooler in Arizona? If it does, the buns will adapt by growing very much thicker fur. They will need some extra food (more pellets or f ex whole oats).
Chickens can’t be kept without extra heating in the winter, but rabbits are very good at keeping warm.