Millennium Snow

Millennium Snow (千年の雪, Sennen no Yuki), also known as A Thousand Years of Snow, is supernatural romance manga written and illustrated by Bisco Hatori. Appearing as a serial in the Japanese magazine LaLa, the nine chapters of Millennium Snow were collected into two bound volumes by Hakusensha and published from November 2001 to August 5, 2002.

Plot
Chiyuki Matsuoka, a high school girl hospitalized with a heart problem. Since birth her heart has been very weak and she was told that she would probably live to be only fifteen. However, one day she meets Tōya Kanō, a vampire, with the opposite problem: Tōya lives for about one thousand years. It's customary for a vampire at his age of eighteen to choose a human partner to be with for 1000 years who in turn would let him drink their blood and share his life span for the millennium.