What about the song he was singing?

Aoi Sangosho was a very popular summer love song. As he lay dying in the snow he may have been thinking of happier times.

"Aoi Sangoshou" http://www.cherryblossom-garden.com/3/matsudaseiko01.html (lyrics found here) is the song they're all singing because like you said Itsuki is (possibly) mumbling it at the last moments of his life. One explaination I can think of is that like his love for the girl Itsuki, he's too timid to express how he feels, about anything. So until then nobody knows he actually loves Matsuda's songs, as he's never told anybody. His consistent hesitance, a quality frowned upon in the West but works for this movie, and believe me, is not hard to find here in Japan.