I believe the Lord had short hair as was the style of the day. back them.
Apparent Shroud-inspired images of Christ are noticeable on coins struck in 692 CE during the reign of the Byzantine emperor Justinian II. The distinctive front-facing appearance of Jesus on the Shroud is also found on numerous icons, mosaics and frescos from the sixth century on. The most startling example is the Christ Pantocrator icon at Saint Catherine's Monastery, reliably dated to 550 CE.
"Using our Polarized Image Overlay Technique, we have examined hundreds of depictions of Jesus in every type of artistic medium from one-fourth-inch-high faces on coins to gigantic mosaics covering the ceilings of great cathedrals from the sixth century on, and we have been able to show that the Mandylion/Shroud face was used as the prototype for almost all of these images."
Mary and Alan Whanger from their book, The Shroud of Turin: An Adventure in Discovery
John 4: 48. Then said Jesus unto him, Except ye see signs and wonders, ye will not believe.