Many premature babies are still covered with lanugo hair at birth, which usually disappears within a few weeks on its own (or about 4 weeks before their due date). (pregnancy-baby.com)
Your baby may also have some fine, downy hair called lanugo all over her body, especially if she was born prematurely. (aboutkidshealth.ca)
Although this is present to a much greater degree in premature infants, term babies also have variable amounts of lanugo present at birth, as evidenced in this photo. (med.stanford.edu)