Baby rabbits should be in a nest with the rest of the litter, inside the hutch. The babies are kept warm through their combined body heat. The mother should be with them in the hutch because she needs to feed them (with her milk) - this also keeps them warm.
If you have an orphaned baby rabbit, you should keep it inside with you because it needs special care. It's not easy to hand-raise rabbits. For the sake of the rabbit, contact a local wildlife rehabber or rabbit rescue agency and ask for help.
Cold weather is a stress on rabbits, and so is reproduction. To limit your rabbit's stress, don't breed her in the winter - only in good weather.
Pet rabbits are most comfortable between 50-75F (10-23C). If your rabbit gives birth in the winter, make sure they're all safe and warm. The hutch should be completely dry (protected from rain and snow), and it should face away from the wind.
When it gets lower than 50F (10C), all rabbits benefit from having a "nest" box inside their hutch (even if they're not breeding). Put hay in it, too - here they can go to snuggle in and warm up.
When it gets lower than 40C, rabbits need to come inside where there's artificial heating.
See the related links/questions below for more details.
A hutch.
By cleaning it.
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Typically a hutch or a cage.
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a cage a hutch
That would be its cage or hutch.
a hutch