Had our first baby 18 months ago. While we weren't charged for skin-on-skin contact, we were charged when the nurse offered to take the baby to the nursey so that mom could rest and recuperate for a few hours.
I can't remember how much it was, but I do remember being upset at the cost...
Also, in terms of out of pocket expenses, I think it really depends on your insurance, hospital, and even the state you live in (here in the U.S.).