Christmas eve here is not a stat day. I normally work until noon that day but this year I have booked it off (unpaid). Boxing day is a stat day in my contract as it is an "optional" day in my province.
If you are already closing wed/thurs I would send a message to your families ASAP saying that you will be closed on boxing day and apologize for the short notice.
If you don't plan to close then I would send out an email saying something along the lines of, "with the holidays being Wed and Thurs some daycare families have mentioned they would not attend the Friday as they will be home enjoying family time. I ask that all families confirm via email whether their children will be in attendance on Friday so I can prepare the appropriate amount of food."
It makes families preplan which helps you while also gently hinting that this is a good time to be home enjoying their family. Won't stop those families that wish to send their kids but might sway a few, and will at least give you a heads up!
If all families state they will not send their children then perhaps on the day you close for Christmas send everyone a friendly email wishing them a great holiday and saying that since all families have confirmed their children will not be attending your doors will be closed and you have made plans for the day. This will prevent anyone from changing their minds last minute and showing up the Friday.
This is just my opinion and what i would do, but i would just take the Friday off. By sending the e-mail and giving the families the choice, you know that "One family" will show up with the kid . It's Christmas, we don't get enough time off with our families