Rabbits do pretty well in the cold as long as they are healthy.
As MH said, kits will die in the cold if the doe doesn't make a nest, or if the kit strays from the nestbox and ends up on the wire floor.
Always keep them covered in the winter. Tarps work well, especially if you cover both sides and the back of the hutch/cage. I like to leave the front open during the day if it's not too cold and then cover the front of the cage at night.
I'm not sure where you live. Where I am the winter isn't too bad so far. There is this 'Arctic Blast' thing that's hitting and the nights are in the teens. My rabbits will have extra hay in their cages on those nights to keep them warmer.
They can get frost bite particularly on their ears. Not sure where you are but it definatly makes a difference. I don't know that a rabbit would do very well without a nestbox or shed to protect against winter weather in northern IN, partiularly if you're trying to breed. Breeding in winter is a challenge even with an insulated shed and heat lamps.