If you have a website you have a storefront on the Internet where your customers come to visit you 24/7. And with those visits come certain expectations.
Posting closings outside of regular business hours is important. Customers expect to be notified on your web pages.
And as mobile phones are used more and more, phone friendly pages, not necessarily completely mobile sites, are required. Let me give you an example:
On President's Day I remembered the library and post office would be closed, but didn't consider that the bank would be closed also. On the banks site that morning there wasn't a mention of closing; I marched off to the bank that afternoon. The first branch I passed was closed. The second branch had closed at 12:00. Pulling up the website on the phone I searched for a list of the branches in the area---found the list---but without phone numbers.
If the phone numbers would have been on the webpage just one click could have gotten a branch on the line so that I could discover if the branch was open.
Instead the bank lost the opportunity to service a customer, even though the bank was closed. Simply by using resources the bank was already paying for a customer could have been served---it wouldn't have costed much additional to post hours; certainly not to post branch phone numbers.