Well, Arakawa has mentioned that Ed's birthday is in winter. We also know that Winry is around the same age as him from the manga. Arakawa hasn't donné us any specific birth-dates for either of them, though.
Hey, at least it gives us fans some wiggle room to play around with! We can have fun picking out our own birthdays for them! =)
That's a good question but why would they even focus on birthdays when Edward and Winry's romance is way better? In the original series They mention Edward's brithday is in winter but I don't know about Winry's in brotherhood ou the orgiinal ou about Ed's in brotherhood.