Many of the islanders have accepted Christmas celebrations has been my experience when in SXM over Christmas. That being said, I do recall a lot of signs by restaurants indicating what type of specials they will have for Christmas, with many taking reservations before and can be completely booked by Christmas. If you have a favorite, try getting in touch with them to see if they will be open and if they plan any specials for that day. As to supermarkets, I think the few that open will close by Noon, but that's probably not true for the Chinese markets.