She's a beautiful mood singer.
That style, I would call Progressive Folk music (showing influence from modern classical music). In some respects it parallels, vocally, what some artists are doing, instrumentally, in Progressive Bluegrass.
As an experimental album track, I think the dreamy, ethereal mood could benefit Carrie in a couple of ways - firstly this type of music has a definite following in Europe (that singer is Scandinavian), and secondly, it could demonstrate her versatility and attract listeners who have reservations about the powerful vocal style and heavy production that's she's best known for so far.
I think, though, that if it were to be adopted, that style would only be an album track, and might not fit well into a concert programme, as it would be a significant change for the two audiences (Country and Power Pop) that have probably formed the core of her existing listeners.
That said, I think it would benefit Carrie to go for a track that did showcase her softer, more dreamy and reflective side - along the lines that she explored in "Forever Changed", for example. Something more like that might suit her own voice more, and could demonstrate versatility without being quite such a departure.
Carrie plays piano, and a well chosen piano backing could work well with her voice. This occurred to me as an another example, by an English singer, who works in both adult Pop and Country and has attracted notice in Nashville, of a type of song that might show a different side of Carrie, but arguably still leave scope for her to show her vocal gifts, without involving too radical a shift in stylistic direction.
