Depends on the school -- Columbia's office is definitely open. A couple of us received "complete" emails from CLS over the past couple of days. I think NYU is also open -- I applied on 12/24 and they requested my report 12/26.
I meant for those schools that are closed for the winter break. Will it matter to them if you submitted your application at the beginning of break or at the end? I'm thinking in terms of what order they review your applications.
Duke's was open yesterday.