Did Jesus have long hair because the Shroud of Turin shows long hair?

Answer:

The Shroud of Turin first appeared in 1354. It is a 14-foot piece of linen cloth with a faint depiction of a crucified man in the stains of the cloth. The Roman Catholic church officially refers to the shroud as an icon, meaning it has a religious significance, but it is not called a relic. Therefore, even the Roman Catholic church is not certain enough to claim it is the burial cloth of Jesus.

Studies of the cloth have been mixed. Luigi Garlaschelli recreated the shroud in 2009, showing that it is possible to create a similar effect without a miracle being involved. A study in 1988 using carbon-dating from three labs showed that the cloth dates from the middle ages (from between A.D. 1260 and 1390). Another study, done in 2013 using infrared light and spectroscopy, dated the shroud between 280 B.C. and A.D. 220. However, the 1988 study appears to have more solid support.

A more recent 2018 study shows that the bloodstains on the cloth are not correct, indicating that they were applied and did not flow from wounds. [Becky Little, "Shroud of Turin Isn’t Jesus’ Burial Cloth, Claims Forensic Study", 31 August 2018].

Historically, there is a letter written in 1390 from Bishop Pierre d'Arcis to the current Pope stating that the shroud was a forgery and that the man who created it had confessed to his work.

There is also the problem that Jesus' body was prepared in a different way than the Shroud of Turin depicts. "Nicodemus, who had first come to Him by night, also came, bringing a mixture of myrrh and aloes, about a hundred pounds weight. So they took the body of Jesus and bound it in linen wrappings with the spices, as is the burial custom of the Jews" (John 19:38-39).  We can see the custom with Lazarus, who was "bound hand and foot with wrappings, and his face was wrapped around with a cloth" (John 11:44). Jesus, too, had a separate face cloth. "And so Simon Peter also came, following him, and entered the tomb; and he saw the linen wrappings lying there, and the face-cloth which had been on His head, not lying with the linen wrappings, but rolled up in a place by itself" (John 20:6-7). Take note that in addition to a face-cloth, there were multiple linen wrappings (the word is in the plural in Greek).  I also wonder why there is no mention of the spices having permeated the shroud.

In the first-century, burials would have been done with plain weaved linen cloths. The Shroud of Turin is a complex herringbone twill weave that did not exist back in the first-century. [Joe Nickell, "Voice of Reason: The Truth Behind the Shroud of Turin," LiveScience.com, 18 March 2005].

What we have is a middle-ages rendition of what people thought Jesus looked like. It matches other artists' paintings in that period. It cannot serve as evidence of what Jesus truly looked like or tell us if Jesus had short or long hair.