It should not be a main cause for concern if your baby has mildly blue hands and feet or if their face turned blue because they are cold or whenever they are crying excessively. The tongue and lips may also turn a little blue when your newborn is crying hard, but once he becomes calm, his color in these parts of the body should quickly return to normal. 

However, seek immediate medical assistance if your baby is having persistently blue skin coloring, especially with breathing and feeding difficulties. This could be a sign that the heart or lungs are not operating properly, and the baby is not getting enough oxygen in the blood.