An Ghráig is earlier than Gráig na Muilte Iarainn as the Irish name of Woodford.
The following is the earliest extant reference to the townland of Woodford / An Ghráig in which the village of the same name is situated: Graige (dated 1667, Acts of Settlement and Explanation). There is an interesting reference to the village in a diary which was written towards the end of the 17th century entitled, The journal of John Stevens, containing a brief account of the war in Ireland, 1689–1691:
"At length having passed what was left of the solitude we came to a small place the English call Woodford and the Irish Graig, where it being St. James's Day we halted and heard mass." page 154 (http://www.ucc.ie/celt/published/E680002-001/index.html).
The afore-mentioned journal refers to the iron-works that were located here: "At Woodford there is an iron work in the bottom upon a small river that falls into the Shannon: the town stands on the hill above it." Further information about the iron-works was recorded by Samuel Lewis, A Topographical Dictionary of Ireland (1837), in an entry about Woodford: 'about 60 years since an extensive iron-foundry was carried on here' (see Information resources, logainm.ie). In the relevant Ordnance Survey Parish Namebook (dated 1837), Woodford was recorded as the contemporary English name and Gráig as the Irish name. The Irish name was subsequently recorded as follows from native Irish speakers in East Galway by the Celtic scholar Heinrich Wagner in 1955 in conjunction with his Linguistic Atlas and Survey of Irish Dialects: 'P(a)ráiste na Gráige' (i.e. 'the parish of...') and also, 'bhí me ar an nGráig inné' (i.e. 'I was in Woodford yesterday'). A member of the Placenames Office, while collecting information towards establishing the official Irish names of post-towns in the district in 1958, recorded the Irish name as Gráig from four informants and Gráig na Muilte Iarainn from two informants (both short and long forms of the name were recorded from a further informant).
The Irish name was published as Gráig na Muilte Iarainn in Irisleabhar na Gaedhilge / The Gaelic Journal, volumes XII and XV. Seosamh Laoide, who was also editor of Irisleabhar na Gaedhilge for a time, gave further recognition to Gráig na Muilte Iarainn in his book Post-Sheanchas (1905), which is a gazetteer of post-towns and various other Irish names. Laoide expressly stated his preference for long forms of placenames. Another Irish scholar, Risteárd Ó Foghludha, also published the long form of the placename in a book entitled Log-ainmneacha (1935). The two aforesaid publications exerted a great influence on the spelling of placenames in Irish.
An Ghráig is the official Irish form of Woodford since 1969. That particular form of the name is on record since the 17th century and it continued to be used by native Irish speakers into the 20th century.