She should only be bringing them inside if there is no other options. If she does she needs to get a shoebox (or similar, depending on her size- i.e. big enough for her to stand in it and turn around), line it with hay, and then transfer as much of the nest as possible. If mummy is highly strung then she needs to stroke mum first. She also needs to make sure either way that her hands don't smell of anything strong (so no predators, no other bunnies, not soap, etc).
As she transfers the nest she also needs to transfer the kits, very gently, with them.
Check all have got bellies that look like they swallowed pingpong balls. Check that none of the bellies have an infected umbilical wound.
If the nest doesn't have much fur you can tease it from around mum's nipples.
Alternatively, if it's feasible, bring mummy and babies in in their current set up- although if they are in something big this may not be feasible.
If mum is unsettled then give her nice noms she can tolerate and make sure to move as much clean contents from cage to cage as possible (so that everything smells ok). Sometimes people put a tiny dab of vanilla just above the nose to eradicate any strange scent- this can work, but doesn't always and can distress some bunnies.
Your friend will have to check to ensure they have been fed within the next 24 hours (if not, she will need to help mum), and if they don't currently look like they have pingpong ball bellies then mum may need to be reminded to feed them. Ensure mummy is having unlimited pellets as well as unlimited hay.
This could be a large danger period, but it may be the only option unless she can do something drastic outside to keep them warmer. A snugglesafe stuck to the underside of wherever they are could work (i.e. not in the compartment, but the heat going through the floor) and reheating regularly including through the night, also making sure the hutch is really, really weather proofed. You can help the nest by teasing mum's fur out and putting it in and also shoving in loads of extra hay so that mummy can keep protecting the nest.
All that said, are you sure they died from the cold and not from, for example, being pulled out the nest or not being fed?