Do you mean in the example above with a snowstorm? All letters and packages would have been dropped off to the mailroom simultaneously and all would have been picked up by USPS/FedEx simultaneously (although if the snow prevented the carrier from getting to the mailroom on that particular day, then nobody’s decisions would have left on time).
Once it leaves PA’s mailroom, it’s out of their control. How long a letter/package will spend in the carriers distribution center will depend on having enough employees coming in to sort, and having truck/planes/drivers/pilots available to take them to the next stop.