Alty, our bunny expert, seems to be off the site right now, but I PMed her, so hope she comes back soon to answer this. As far as I know from her previous answers, bunnies need a good heated shelter and/or a warm room, like inside instead of outside. They are domestic, not wild, and are used to being indoors.
Yes, rabbits can die if they're too cold. Think about wild rabbits. They live in burrows underground, in warrens (groups). A burrow is actually very warm, especially since there are many other rabbits living there, and body heat alone makes the area warm.
With domesticated rabbits we've forced them to live above ground, usually alone, in the wind, snow, and other conditions. This can kill a pet rabbit.
Rabbits simply aren't equipped to handle the extreme cold. Even in a good hutch, well insulated, and well kept, if the weather is too cold, bunny could die.
Also, I just want to add that Fr_Chucks suggestion of having more than one is a good one, but make sure that both rabbits are spayed or neutered. Not only because it's better for their health, but to prevent an unwanted pregnancy.
I have one female rabbit and one male rabbit to keep me happy, but I think their babies will would keep me happier.I want my rabbits to have babies, but every time they do have babies the babies die.First when the babies were born they were breathing and moving, but the next day they all died.I...