If I were to guess where that music was coming from, I would think it would come from another Newman score, the closest one to Phenomenon and The Horse Whisperer being The Shawshank Redeption.
The music in the trailer for The Horse Whisperer is from the score to The Piano like the above post says. I have looked around a bit and from what I have found (at filmmusic.com), the music in the trailer for Phenomenon is by Enya and it is called Book of Days.