When my husband was a teenager he spent a weekend camping out in the snow to earn some kind of Boy Scouts award. At the time his feet and fingers went numb, but being a boy and a teenager, he "toughed it out". Ever since then, though, his feet and hands turn icy and blue even in cool, not cold, weather. Please do go have your fingers checked out by a doctor.
Do have them checked out to determine if it is frostbite or if you might have something else going on.