Actually the Veil was worn by Christians in Byzantines as a sign of status and wealth and that's where it originated, Zoroastrians didn't wear it - at least not on Ancient Sculptures in Persepolis.
My understanding, though, is that Persian society, having been heavily influenced earlier on by Hellenic culture, pretty much sequestered their women away - just as Arab society does today, but back in Mohammad's time, it didn't.