Newborn arm flapping?

So since day one my newborn has been shaking/flapping his arms. He always has done this, even in the womb I often felt a tickle and wondered what it was. As soon as he was born I knew. It's almost like he's cold when he does this. He had his blood tested for sugars, etc at the hospital and they said everything was fine. He constantly has his hands by his face as well. Is this normal for babies?