When I had a litter of 7 puppies earlier this year, (no it wasn't freezing) I would get up and take all 7 out to toilet when I heard them on the newspaper. They were in a large C-Crate and could toilet away from their sleeping area but preferred not to & I thought this was a good start for their prospective new owners.
However they were returned straight to the crate the minute they had finished. Ignored and I went back to bed.
Regardless whether it was freezing or not I would do the same, they have each other for company and body warmth and provided they have blankets and the crate is covered they should resettle and be nice and warm.
But if your happy to have them in bed with you afterwards that's fine everyone has their own rules and expectancy from their dogs.
If I can't watch a puppy during the day then it is put outside. The more times it goes to the toilet on it's own outside the better. Toilet training is best dealt with repetition.
Good luck with your little pack and please don't forget to post some pictures.