Will my rabbits babys be ok?

my rabbit has just gave birth,but she lives outside and im scared the baby's will get to cold and die. i have gave her plenty of hay which she has put in her nest and she has covered the baby's up with fur i have also covered up the front of the hutch where the meshing is with an old rug to keep the wind out. i don't want to move her hutch into the garage because then i will be scared that she will eat the baby's because i have moved her from her territory. will the baby's be ok through the cold weather?