Trelawney and birthdays (mix-ups?)

[Inge]

No: HPFGUIDX 134223

I should have my books at hand before posting - I know. Happens so that 
right now I don't - and if I wait with the posting I will have 
forgotten about it....
So...

In one book Trelawney adresses Harry in class and asks if it isn't true 
he's born around Christmas (or at least at winter-time - sorry I don't 
remember). 
Harry laughs - of course he's not born at winter.

In HBP it turns out Tom Riddle is born on New Year .... 
Could Trelawney somehow have gotten some sort of her mistaken birthdate 
for Harry from Harry himself? Did she look at Harry and sensed the part 
(Horcrux) of Tom Riddle inside him and therefore made the birthday-
error?

Inge