[Formendacil]

We are never told- I believe.

However, it seems logical to assume that a fair number, if not the majority, of the Iron Hills Dwarves remained in their homehills after the War. The Dwarven colonies in the Iron Hills go back to the First Age, according to Tolkien's essay "Of Dwarves and Men" (HoME XII), when the Longbeards ruled most of the non-forested (ie. Mirkwood) parts of Wilderland, from their chief city-delving in Khazad-dûm, north to Gundabad, and thence eastward, including the Grey Mts, as far as the Iron Hills.

It seems clear that the Longbeards maintained a presence in the Iron Hills through the fall of Moria, the movement of Thráin I to Erebor, the subsequent movement of his heirs to halls in the Grey Mountains, their hasty return back to Erebor after dragons sacked their halls, and their wanderings after the expulsion of Thrór.

After such a long presence in one area, I highly doubt the Dwarves would leave. They were very "stick in one place"ish to begin with.