Wild rabbits and pet rabbits can live outside during the winter, because they do not typically hibernate during these months. Their thick coats allow them to stay outside during the cold months, but it does not completely protect them from all of the elements.
In the wild, rabbits typically don't go into a true hibernation status during winter. They will usually forage less and stay in their burrows more during the winter months but will come out to search for food on occasion. In extremely cold temperatures, rabbits will stay in their burrows more because it is warmer under the ground.
The traditional housing units for pet rabbits are hutches. These hutches are comprised of an outdoor area and an indoor area and are often raised up off the ground. The indoor area provides the small amount of shelter a rabbit would need during the cold winter months, while the outdoor area gives them room to enjoy the fresh air.
Another option for a pet rabbit would be keeping it inside the owner's home. Pet rabbits can be litter trained, so they don't always need to be in a cage when they live in the home. It is important to note that a pet rabbit that is accustomed to living in the home should never be let outside during the cold winter months.