Five kinds of piece
The national list says the older pieces mostly grew out of folk songs and fall into five classes: songs kept close to their vocal form, tunes from heroic epic, horse-pace tunes that depict the horse, instrumental pieces developed from songs, and old Han tunes such as Pu'an Zhou. The page's examples include Zhuose Lian and Bayaling in the first class, a running-horse tune in the second, and Heyinhua in the fourth. The instrument is played at formal occasions and at weddings, alone or under a voice.
The page's own warning
The same entry says there were four traditional schools, each with its own pieces, and that today the inheritors are few and the loss of repertoire is serious. That sentence is more useful than a praise-word. It tells a reader the instrument is not a completed souvenir. The listing date is 2006, the first batch, for the autonomous region. A related entry on the same page names Mongoljin morin khuur music for Fuxin in Liaoning. It is not the body of this listing.
The name stays with the listing
This page does not stop to explain the horse's head on the pegbox. Other pages do. Using them here would glue a sentence from a different entry onto this one. The solid content is the five classes, the four schools and the admission that the repertoire is thinning. The long song, listed in the same year, is the voice this instrument often sits beside.