Herod's Temple is actually the same as Zerubbabel's, still officially considered the "second Temple." But in the first century A.D. Herod greatly enlarged upon the Temple then in existence with a grand remodeling scheme. The building project lasted for decades, and it is "Herod's Temple" that we find in operation during the ministry of Jesus. This is the Temple that Jesus cleansed and at which He spent much of Holy Week teaching and preaching. The disciples commented on what a majestic wonder this Temple was, and it served as a cradle for the meeting of the early Christians in the book of Acts. So is it possible that this massively remodeled building was what Ezekiel had in mind in chapters 40 to 47?
Again, the answer appears to be no.
As a potential candidate for Ezekiel's Temple vision, Herod's Temple suffers from the same inadequacies as the others. It is not the right size - it does not fit with the description or square with the details of the text. Ezekiel is simply describing a radically different building that what any of these actual, physical Temples resembled.
Herod's Temple did not last long. Following a Jewish rebellion, it was reduced to rubble in 70 A.D. by the Romans. No other Temple has been built on that site, but now the Muslim site known as the Dome of the Rock occupies the Temple Mount.
Despite all previous incarnations of the Temple, It would seem that Ezekiel's vision has never yet been realized in the physical world - if that was its true intention.