With my 1st c/section for the twins (36 + 3 weeks) they took the babies away for around an hour into special care to warm them up so that wasn't nice. We half expected this to happen again at the c/section of our little guy but we were very pleasantly surprised when we were able to keep him with us - literally on my chest wrapped up until we got back to the room then they stripped him off and put him on my chest

Mind you he was over 9 pound so I suppose he had enough covering!
We are now expecting twins again in about 4 weeks and who knows what will happen in the operating room?? What I did find really supportive and helpful was that my husband was asked, with our twins, if he would like to go with them to the nursery or stay with me after the c/section and he stayed with me in post op - this really helped as I would have been very lonely!!!
Good luck.