I had a friend at school who was born on Christmas Day but she kept this very quiet for some years, until someone discovered her middle name was Noelle and her secret was revealed....
My sister-in-law's birthday is the day after Boxing Day and absolutely, she gets separate cards and presents. It's really mean not to, I think! You can't help what day you were born on after all.
I know someone born on xmas eve and someone born on boxing day. They both complain about a lack of presents. I had a cat that was born on xmas day and he never got two presents but he didn't seem to mind.
I don't know anyone born on Christmas day, but my nephew is born on New Year's Eve. I always make an effort to do separate presents for him (if it's a year that I'm feeling motivated to do presents!). My sister and cousin were both born on the 2nd of January and the biggest complaint has always been that they can't have a party as that's smack bang in the middle of school holidays - of course now they are adults they can have a party!
I have one friend whose sister's birthday is the 24th, and the brother Boxing day, and another friend whose teen son is Chrismas day, with my dad on the 27th.
The first friend's family often have a three day celebration as she is an Anglican priest so is busy anyway around that week.
The second family sometimes have Christmas on the 24th to give the boy a full birthday the day later.