Itsuka Furu Yuki

The protagonist is a doctor that's got a new job at a small out-of-the-way sanatorium for the terminally-ill. He goes there but is surprised to find the place is practically empty, except for a handful of patients and one other doctor (the doctor that hired him is busy and doesn't even bother to come say hello). The title comes from the main heroine, who has a debilitating brain disease that's in the end stages and is losing her long-term memory. She's going through the days in the hope that before she passes away she'll get to see the snow again, because in her diary she wrote that the snow was beautiful and that she really loved it, but she can't remember what snow is like anymore.