My roommate, Penny, her sister, Kitty, and our friend, Chelo, do our gift exchange on Epiphany.
Chelo is Spanish/Filipino, and was telling us that when she was a kid in the Philippines, Christmas Day was strictly a religious holiday, church, etc. But on epiphany, they went to the Spanish Club and the wise men arrived on their horses, not too many camels in the islands, and distributed the gifts to the children. We thought this was a great idea, so now we get together at one of our homes and have dinner prepared by the hostess that year, and do our gift exchange. I think we enjoy it so much more because the rush is over and we really have the time to spend with each other.