The closest thing to a physical description of God in the OT/Hebrew Bible, is this passage from the Book of Daniel (7:9): As I looked, thrones were set in place, and the Ancient of Days took his seat. His clothing was as white as snow; the hair of his head was white like wool. His throne was flaming with fire, and its wheels were all ablaze. river of fire was flowing, coming out from before him. Thousands upon thousands attended him; ten thousand times ten thousand stood before him.
So, old, male, dressed in white, white woolly hair. This is basically the only description artists had to work with when the taboo against depicting God was overcome.
In Revelations there is a description that almost exactly matches the one in Daniel, except for the important difference that the character described is a "Son of Man", presumably Christ:
(Rev.1:12) I turned around to see the voice that was speaking to me. And when I turned I saw seven golden lampstands, and among the lampstands was someone like a son of man, dressed in a robe reaching down to his feet and with a golden sash around his chest. The hair on his head was white like wool, as white as snow, and his eyes were like blazing fire. His feet were like bronze glowing in a furnace, and his voice was like the sound of rushing waters. In his right hand he held seven stars, and coming out of his mouth was a sharp, double-edged sword. His face was like the sun shining in all its brilliance.
Of course this is not the everyday Jesus a the time of his ministry in Galilee. This is the resurrected Christ ruling the heavens. Still, this is the only physical description of Jesus in the Bible, so again it had a big influence on artists.
From what I understand, the traditional / classical image of God as an adaptation of Zeus / Jupiter occurred along two timelines:
The first was at the spread of Christianity through the Roman Empire, where analogs were generally adapted / evolved. The temptation of the artists were to transmogrify the existing image of the Roman gods into those of God (Jupiter / Zeus) and Jesus (Apollo), though this was frowned upon to the point of myths arising about artists hands withering as they attempted to do so. That said, artists persisted in adopting the motifs, even if they had motives more aligned to those of the emerging church, namely a "defeat" of the old gods by the christian gods. Commandianus, one of the Nicene fathers, even writes about how God is greater than Jupiter, while still anthropomorphizing him in The Instruction of Commandianus. The prayer of Licinius's army was left ambiguous as to the god, per the scholar in this book
This was further exacerbated in the renaissance, when the recollection to classical themes took place concurrent to a time when the Christian church did not lack for power. Artists looked to comingle the two. A good example of this is De Partu Virginis (1521) which adapts Virgil's Aeneid, but plays off its Christian-analog themes to paint the epic as an ode to Christ (a not-unique effort; note Virgil as the chosen guide of the underworld in Dante's inferno) - the argument is well articulated here.
I don't have my books on the continued weaving of the images together, but there is siginificant literature on the influence of the greco-roman aesthetic on european, christian art. Considering the low degree of literacy throughout much of European history for the common people, it is unsurprising that an image-based representation of God would instantiate itself into Christianity, regardless of how closely it tied to the (fairly sparse) descriptions of God in the bible.
In the Mosaics in the antechamber of Saint Marks cathedral in Venice there is a genesis narrative and God was a brown haired man who is clean shaven. The artist is unknown from around 1250.
http://2.bp.blogspot.com/-l0Q7wdvGmGw/URWPJG_SF1I/AAAAAAAACR0/ojpgTT5CMuM/s640/Green+%2526+Gold+Dome+Basilica+di+San+Marco.jpg Here is a link, but it is a bit small. However you can probably see that god has no white beard.
Question: would it have anything to do with the fact that religion started out as ancestor worship in which the designated priest would communicate with the dead elders of the tribe?