It seems that in art, ancient architecture (columns, marble, etc) goes hand in hand with paradise. Is this simply a romanticizing of the ancient "golden age" of the Roman Empire by Medieval Europe?
Understanding representations of a Christian “heaven” is fairly complex. It is possible that the tradition which you mention is linked to the conflation of Roman imperial imagery with that of the “heavenly” Jerusalem beginning in, roughly speaking, the 4th and 5th centuries. I may be of some help in regard to “heavenly Jerusalem.”
The earliest extant visual depiction of Heavenly Jerusalem is the apse mosaic of Santa Pudentiana in Rome, dating back to around 402 and 417, under Pope Innocent I. Here, scholars generally agree that the setting is in heaven, with a mixture of apocalyptic and Constantinian components. Regarding the apocalyptic elements, we have the four beasts in the clouds, the gates of the city which were mentioned in Revelations. The city itself is constructed in a style reminiscent of Constantinian architecture; we have the Anastasis-rotunda of the Church of the Holy Sepulchre on the left side, Golgatha in the middle, and the decorated cross. These allusions suggest that the Constantinian style of earthly Jerusalem completes the apocalyptic image of the heavenly.
A useful comparison of these sorts of congregational scenes would be from the catacombs of Santi Pietro e Marcellino. Christ again is depicted with the Apostles and the lamb is again underneath his feet (which is also in the apse mosaic, but too difficult to see), but notice the absence of any defined background. Both the upper and lower registers have Christ and the disciples on some sort of ground, but, unlike the apse at Santa Pudentiana, we don’t have a clear setting, and we can’t extrapolate whether this is Christ as rex or Christ as iudex. Likewise, another 4th century mosaic lacks any of the detail found in the one from the St. Pudentiana apse. The detail of the apse mosaic, then, with its apparent setting in a Heavenly Jerusalem, complete with apocalyptic and Constantian allusions, becomes rather stark and the innovation rather clearer.
Such a connection to imperial architecture, as in the case of the apse mosaic, is not an isolated occurrence; in fact, this program becomes much more manifest in fourth century representations of Heavenly Jerusalem. We need only to overview Constantinian building projects, the Church of the Holy Sepulcher in particular. As the story goes, Helena, the mother of Constantine, discovered the tomb of Christ in Jerusalem, the site upon which Constantine ordered the construction of the Church of the Holy Sepulchre. It was composed of three types of buildings: the rotunda, as a monument to the resurrection; the inner atrium, in the memory of the crucifixion on Golgotha, and the basilica itself. The Church is a manifestation of the New Jerusalem, according to Eusebius (ἡ νέα κατεσκευάζετο Ἰερουσαλήμ, Vit. Const. 3.33); but it also shares a general connotation of Heavenly Jerusalem on earth. This is in large part the function of churches themselves but also, in this case, the unique location of the Holy Sepulchre in Jerusalem. The unifying cross in the apse mosaic, which links heaven and earth through Christ, is essentially embodied via the Church of the Holy Sepulchre; heaven and earth are linked with Heavenly Jerusalem on earth.
Nevertheless, though depictions of Heavenly Jerusalem are limited in Late Antiquity, it is still helpful to see how these previous notions developed in later periods. The eschatological motif in depictions of Heavenly Jerusalem does not taper off, and illustrated Apocalypses are quite common during the Carolingian period. The Palatine Chapel with its iconography heavily drawing from the Book of Revelation, is a testament to this notion.
The aforementioned apocalypses show that attempts to portray the Heavenly City were a marked departure away from the Apse mosaic from St. Pudentiana; while the apse mosaic tried to follow the Revelation of John rather closely, the illustrated apocalypses try to imitate the book more in spirit. The Apocalypse of Trier is considered to the earliest of these manuscripts, and, 100 years later, it was copied in Northern France. This Heavenly Jerusalem is on high brick foundation, is circular in shape, as opposed to the perfect square in Revelations, and has twelve towers enclosing two churches in the center. One of these churches has a domed rotunda, an allusion, perhaps to the Holy Sepulchre. The Greco-Roman architecture, which seemed more prominent in Late Antiquity, actually begins to shift towards something that looks more contemporary.
There also appears, in some cases, especially toward the end of the first millennium, a union of sots between Old Testament ideas and Heavenly Jerusalem itself. Observe, for example, the following images. The trend to depict Heavenly Jerusalem as a contemporary medieval city can be illustrated well from a depiction of Saint Simon on the 9th century Chludov Pslater. Unfortunately, I don’t have a digital image available. In front of the city is King David, holding an icon of Mary and Christ; towering over the fortifications are lofty buildings and the Church of the Holy Sepulchre; the only way to enter this Heavenly Jerusalem is by climbing a small ladder. Again, the tie between Heavenly Jerusalem and the Church of the Holy Sepulchre, which we saw begin in the Apse mosaic, continues into the 9th century.
Put simply, I think it would be wise to say that depictions of “heaven” varied, depending on the allusory intent of the artist. As stated before, the conflation between Jerusalem and heaven was fairly prominent. The construction of the Church of the Holy Sepulcher, in conjunction with its association with an increasingly Christianized Roman Empire, most likely contributed to the development you mentioned. Nevertheless, we still see “heaven” depicted as a contemporary medieval city in some cases, so it’s hazardous to universally equate it with Classical architecture.
Select bibliography
Copeland, Kirsti B. “The Earthly Monastery and the Transformation of the Heavenly City in Late Antique Egypt.” In Heavenly Realms and Earthly Realities in Late Antique Religions. Ed. Ra’anan S. Boustan and Annette Yoshiko Reed. Cambridge: Cambridge University Press, 2004.
Ćurčić, Slobodan and Evangelina Hadjitryphonos, ed. Architecture as Icon: Perception and Representations of Architecture in Byzantine Art. New Haven: Yale University Press, 2010.
Du Bourguet, Pierre. Early Christian Art. Trans. Thomas Burton. New York: Reynal & Company, 1971.
Grabar, André. Early Christian Art: From the Rise of Christianity to the Death of Thodosius. Trans. Stuart Gilbert and James Emmons. New York: Odyssey Press, 1968.
Kühnel, Bianca. From the Earthly to the Heavenly Jerusalem: Representations of Holy City in Christian Art of the First Millennium. Rome: Herder, 1987.
Safran, Linda, ed. Heaven on Earth: Art and the Church in Byzantium. University Park: Pennsylvania State University Press, 1998.
EDITS: Formatting, and retrieving the Eusebius quote.