We have discussed here many times that based on genetics the most important ( since Neolithic ) migrational event into Armenia occured at MBA (circa 2400-2200bc). The supposedly source of migration is the Catacomb culture in the North then via Daghestan.
According to this paper they introduced also brand new horse haplotypes in South Caucasus and Anatolia.
PS Horses were present in Armenia before MBA but they had fewer haplotypes. https://www.science.org/doi/10.1126/sciadv.abb0030