yeah i've pretty much always celebrated the following week, I have a cousin who is 10 days younger than me so our first 2-3 birthdays got shared. Jan 5, just because it was easier to get the family together once, compared to twice. Sure I always had some sort of immediate family celebration albeit really small, on my actual birthday maybe one gift, but usually gifts waited until january since it was so shortly after christmas. 

"Oh it must be cool, you get twice as manygifts..." not really people, the X-mas gift money gets split between X-mas gifts and birthday presents when your birthday is so close.