Should I shower my baby while he's asleep?

My boy is 1 month old & recently, my parents said I shouldn't wipe his face or shower him while he's asleep. I should wait for his awake window and shower him. But the concern I have is what if by the time he wakes up, the weather gets too cold for a shower. I tried waking him up but he's too drunk to even open his eyes. If this is true, what is the rationale?