
I interpreted ‘closing’ as a permanent state – as in closing down. I would have thought that ‘We will be closed on 25th December’ as the appropriate to identify the days upon which they would not open.
We did eat in the restaurant after Christmas so we do know that it did not close down.
Maybe it is by signs and usage such as this, that ‘closing’ and ‘closed’ may come, in time, to mean the same.