Sims are freezing to death

I wouldn't bother about that if it were me.  Babies can't die from it.  You are correct though; the freezing and overheating buffs should go away soon after you turn the heat on so they shouldn't be there for more than a few hours.  But buffs do get hung on sims sometimes.  There's not anything that I know that can do to get rid of them if you play without mods.  There are few mods that allow you to get rid of them if you do use mods.  UI Cheats can do it for instance.  I'm not sure you can do that for babies anyway.  I think it only works for infants and above. Otherwise, you have to wait them out.  Since yours are babies, they might go away when you age them up to infant or if the season changes to Spring.  

I assume the adults are the babies' parents.  So, if both continue to die as soon as you load into the lot and there is at least one sim remaining in the household that is teen or above, you could just let them die and then resurrect them or just continue to play them as ghosts once you get them to join the household again.  Once you get a ghost to join a household, they become playable again, so you have plenty of time to resurrect them later and just play them as ghosts in the meantime.  Otherwise, you will need to make Ambrosia or, if you have the Romantic Garden pack, use the wishing well.  If you don't have another teen or above, then you can temporarily move one in to keep the Social Worker from taking the kids away and to ask the ghosts to join the household.  I haven't had that happen in a very long time so I'm not sure what happens in that case, but I seem to remember that if both parents die and no other teen and above sims are in the household, then you might get kicked back to the world screen and the kids simply disappear from the game.  I might be completely wrong on that as the game has changed a lot since I last had it happen.  And it is my understanding that if you have the Life and Death pack and have a will, then the kids might be sent to live with whichever household that the will has designated.  Again, I am not sure on that since I haven't had that situation in my game nor have had a sim make a will yet.

Hope this helps.