Babies’ appearance varies and changes over the first hours and days. Immediately after birth, because they have been in a bag of fluid for the last 9 months, babies have that wrinkly appearance that you get from being in the bath a little too long. As their skin adapts to being in the outside world the wrinkles disappear.
If a baby is very overdue then the skin can appear quite dry and in most cases will flake off, as with all dry skin it can appear wrinkly due to the lack of moisture. Once the skin starts to flake there is nothing to be done to stop it just continue to use water only on the skin and the layer of skin underneath will be fine.
Avoid anything but water on babies skin for bathing in the first month, if you want to do baby massage after bathing pure vegetable oil is the best to use, avoid any nut based oils or mineral oil as they can be harmful to baby’s skin.