Does anyone know the name of the song played in these scenes from Dagashi Kashi? In this clip from Dagashi Kashi the song starts at 0:15, and in this clip it starts at around 0:58. I tried searching for it but couldn't find it anywhere. Does anyone know the name of the song?

EDIT: Both clips are from season 2. First clip is from episode 12. The scene is at the start of the episode around 0:38. The second clip is from episode 4. And starts around 11:35 in that episode.
Fuyu no Ame is the first song, it is from the second season soundtrack.