If I were to listen in the hills, Mendelssohn would be a fine choice. However, I too prefer to listen to the world around me, or to the silence on those rare still days.
Where I do enjoy music that evokes the hills, folk and certain classical, is afterwards when the wind is howling against the windows, the fire is on and the memories of the day on the hill are somehow enhanced. This is especially true in bothies or the more basic hostels (we'd never impose it on others though).
I also like to take my guitar and do some folk stuff whilst out wild camping in the canoe, it works for me then. My companions' opinion may differ, but I haven't been buried in a shallow grave yet because if it