I had remembered that Ed was 15 in the series, then I realized that I had no clue how old Winry was! Does it say anywhere how old she is, or do they just give an estimate?
You can check the FMA Wikia
Her year of birth is mentioned as 1899, which is the same as Edward's, although their exact birthdays are never stated. She is 15-16 years old during the course of the manga/anime, and around 18 post-timeskip.
MyAnimeList lists her exact birthday as June 9th, 1899. However, I don't know if there's any credible source for that.