Regarding hair length, the idea of shoulder length hair for the Christ seems arguable, insofar as long hair was considered improper for men : an example can be found in 1 Cor 11:14-15 :
Does not the very nature of things teach you that if a man has long hair, it is a disgrace to him, but that if a woman has long hair, it is her glory? For long hair is given to her as a covering.
Regarding beard, it is well established from Jewish sources that it was a virtually omnipresent male attribute, making it extremely likely that Christ would have been bearded.
As for hair length, yet, as you may know, there is debate as to whether Jesus was considered a נזיר (nazir) : a Nazir was a Jew who committed to a separated (nazâr) life from the rest of the community and chose to abide by strict laws of purity. The specific rules for such nazirs are detailed in Nb 6. 1-21 : they include no alcoholic drinks, no hair cutting or shaving, and no contact with corpses (among other things).
The question of whether Jesus was a nazir comes, among other facts, from the designation in the titulus that John says Pilatus wrote and had apposed above the Cross, which said "Ἔγραψεν δὲ καὶ τίτλον ὁ Πιλάτος, καὶ ἔθηκεν ἐπὶ τοῦ σταυροῦ: ἦν δὲ γεγραμμένον, Ἰησοῦς ὁ Ναζωραῖος ὁ βασιλεὺς τῶν Ἰουδαίων."
The translation usually goes as "And Pilatus then wrote (Ἔγραψεν) a titulus, and put it upon the Cross, there was written : "Jesus the Nazarene, the King of Jews". Not to enter into further detail as to the detailed theological implications of the titulus (another topic of debate lies within the different languages in which it was written, as John says later, and in particular, what was the Ἑβραϊστί language : Aramean or Hebrew), the question is whether Ναζωραῖος does mean "the Nazarene" (as in "originated from Nazareth") or something else. The idea that Pilatus would have bothered writing the small village in upper Galilea where Jesus supposedly came from does raise questions. The idea regularly comes that it might have meant that Jesus was a committed nazir for life (usually the nazir vows were limited in time but other Old Testament characters such as Samuel or Samson, whose story famously features long hair were nazirs for life). Tresmontant in Christ Hébreu (1983) and S. de Faytaud in Les actes de Jésus (1994) detail this theory and are in general support of it. Christophe Lemardelé in Les Cheveux du nazir underlines that conflicting etymologies do not favour this solution. In any case, this interpretation has deep (and obvious) theological implications : Samuel, an other Nazir for life, was both a priest and a prophet (the first of the prophets and the last of the Judges), and, along with the idea that Jesus was king of the Jews, this underscores the idea that Jesus is Priest, Prophet and King (a recurring idea in Christian theology, memorialized in Baptism in the Roman rite). The connexion with other saviours (such as Samson) would also have been alluring. Finally, the idea that he was separate from God's people, while it's most consecrated element, has christological allusions.
Now regarding iconography, we know that the earliest depictions of Christ would have portrayed him in the Roman fashion, as a clean shaven and short-haired man. For instance, the depiction of the Good Shepherd, in the mosaics of the Mausoleum of Galla Placidia, in Ravenna, dated 450 AD, show such a portrayal. Similarly, in the IVth century sarcophagus of Giunius Bassus, preserved in the Rome Museo della Civiltà Romana, Christ has no beard. This clean shaven look would have made Christ look very different from pagan gods or Greek philosophers or eastern magicians and divinators as they were always shown with a full beard (save for a few gods like Apollo). In the second half of the IVth century in the Mausoleum of Constance in Rome, Christ is again beardless.
Around the turn of the IVth century,Christ became more and more depicted as a bearded man, probably with Eastern Christian influences, as the traditional eastern tradition depictions retained bearded images of Christ, with attitudes and structures still present in modern day icons : as an example, the VIth century encaustic icon from Saint Catherine's Monastery in Sinai (Egypt), the oldest surviving panel icon of Christ Pantocrator, is already very typical.
In Western Europe, beardless depictions of the Christ remained, although rare, until the IXth century : an example is the Évangéliaire de Godescalc, a manuscript kept in the Bibliothèque Nationale de France, which shows a beardless Christ in the Pantocrator attitude, which is very unusual.
