Kits can't regulate their body temperature themselves until they're a couple weeks old and rely on mom's fur in the nest and snuggling together to stay warm. One thing to consider is whether your nest box is too large - it should be big enough for the doe to turn around in, but if it's too big then the kits might spread out instead of sharing body heat. Also make sure that the nest box is designed in a way that prevents the kits from getting out until they're around 3 weeks old.
Insulating the hutch to maintain as much warmth as possible and prevent drafts is even more important with kits than older rabbits.
Depending on your climate and whether the hutches are fully outdoors or in a barn/shed/garage of some sort, bringing them inside may be necessary (if not full time, then at least at night when the temperatures are lowest). You can bring mom and kits in or just the nest box (if you only bring the nest box, make sure it's not inside for too long as mom normally nurses the kits 1-2 times a day, in the late evening and/or early morning).
Make sure it's not too warm in the room if you bring mom inside, because she'll have a thick winter coat and can overheat easily at much lower temperatures than usual - monitor her for signs of overheating/being too warm.
Many people that breed who live in a place with cold winters and keep their rabbits outside don't breed at all during the winter (conversely, people may not breed outdoor rabbits during the summer in very hot climates) and plan their first litter of the year for the beginning of spring.
As Jbun pointed out, unlike some animals, mother rabbits will NOT reject their babies just because they've been touched by a human. Kits can be safely handled from the day they're born. If the mother seems agitated at all when you go to handle them, let her out of the cage/hutch and put her where she can't see it before handling the babies - they won't reject babies over your smell but may reject them if they feel stressed out.
Handling the kits every day is important - this lets you check to make sure they're warm enough, that they're all being fed and that none have died.
It's not uncommon for a doe to lose or reject her first (or even second) litter. Most breeders play by a "three strikes" rule - if a doe hasn't learned how to be a "mom" by the time she's had three failed litters, she's removed from the breeding program (ie retired from breeding and kept as a pet or placed in a "pet" home).
