The basic idea is that a small group of people, that were infected by the virus but managed to survive, has their hair colour changed to white and their eye colour changed to green. Said traits would then be passed on to future generations.
Some context info (changeable if needed):
1 The affected group is ethnically pure = physical traits vary less (think modern-day Japan).
2 Eye colour has changed from blue to green; if not green then gray.
3 These traits aren't dominant (this comes from my very crude understanding of genetics); a kid would need both of his/her parents to be affected by the virus to be fully white-haired/green-eyed.
4 The virus has a kill-rate of 90%.
5 The world is comparable to Europe's late Medieval Era.
6 There's no magic.
7 The virus is transmitted through the air.
8 It is naturally occurring.