My DD was born in a hospital and had to go to there level 2 nursery for a few hours after she was born (had a medical issue we had not known about ahead of time... long story). Anyway, they did a bath there. I don't know if it was policy but I remember being a bit annoyed in the morning when I went down there to nurse her and they told me they had given her a bath. No one had asked or notified us or whatever. She was born at 2am and this was during around 4am - 6am when we were sleeping so they maybe just didn't want to wake us up... I never thought about it being policy for the nursery though.
This time DS was bathed about 10 hours after he was born in the hospital but they asked us first and seemed fine either way. The nurse had actually said that he looked pretty clean and we could just do it at home when we felt like it and I was ok with that but DH is more of the easily grossed out type and really wanted him bathed so I was ok with it. They actually did the bath while under the warmer so that the body temp would not go down too much.