I have never known someone who would reject a gift because it didn't happen to be given on their gift-giving holiday. At my office, people often bring in special foods to share which are associated with their holidays, be it Rosh Hashanah, Eid, Diwali, or Christmas. What is not appreciated is the assumption that you share the same holiday.

Business is business - it is not a gift. It should be for value received. If the OP wishes to give gifts to some of those who have made his life more pleasant this year, why shouldn't he?