I used to raise show rabbits in Utah... the winters were pretty severe where I lived way up in the mountains.
What is hard for rabbits is HEAT. The cold they can handle just fine. (One exception. I knew a lady who SHEARED her Angora in the MIDDLE OF WINTER. It died! Big surprise! So NO, you can not cut off all their hair in the middle of winter and expect them to survive!!!) I had a barn that had a roof and 3 solid sides with good strong wire on the front (to keep out raccoons and other predators). This had excellent ventilation. You will need to protect from predators. I did lose rabbits to having raccoons grab them and pull off a leg or something. You get up, the rabbit is not dead yet, you have to put it out of its misery... not a pretty sight.
I raised: Mini Rex, English Angora, French Angora, Silver Fox and Tan. They all did great. Because my barn had a nice big roof they were in the shade in the summer and stayed pretty cool. Some people will put fans in their barns if the weather is too hot. Again: it is the HEAT that is hard on rabbits. Not the cold. Just like chickens they need to stay dry, and have good ventilation. My cages were all hung at least 2' above the ground so the droppings would fall far from the rabbits. I would then rake up under the cages. Do not let them sit in wet bedding.
My rabbits did so well that I won enough ribbons to make a quilt out of the ribbons. A king-sized quilt. I see no reason at all why you could not do even better than I did.