I'm not sure that's entirely right. It's my understanding that there was already a trend towards shorter hair styles and a clean-shaven look years before the war started, although I don't have a specific reference I can point you to for that. I certainly don't recall from memoirs, letters or other sources any complaints from soldiers who found themselves having fashionably long hair shorn off upon volunteering/conscription in the way that some men joining the services for Vietnam in the 1960s/70s bemoaned the buzz-cuts they received on arrival for training, when hair fashions were typically longer.

However, Peter Englund has a specific claim on this issue:

Head wounds were much more common than in earlier wars: the troops were now spending much of their time in trenches where, for obvious reasons, the head was the most exposed part of the body. The custom of cutting the hair short was introduced during the First World War, not (as is often assumed) as a way of dealing with lice but because it made the treatment of head wounds faster and simpler.

The Beauty and the Sorrow: An Intimate History of the First World War by Peter Englund, Profile Books, 2011

I don't entirely agree with this claim, though. The pre-war King’s Regulations (for British soldiers, all ranks) demanded that:

The hair of the head will be kept short. The chin and the under lip will be shaved, but not the upper lip.

The (rarely enforced) moustache requirement was dropped in 1916, but as far as I know there was no requirement for hair to be shaved short all over introduced at the same time for the sake of making the surgeon's life easier: the requirement was simply the vague "will be kept short", which might be best interpreted as 'short back and sides'. If anything, there was a trend to keep the hair on top a little longer to help maintain some semblance of individuality. For example:

Hair oil was widely used by officers, who had an insatiable appetite for the Jermyn Street fripperies that somehow made life more bearable, though one officer gave up wearing it when he found that it encouraged rats to nibble at his head.

and:

Younger soldiers often sported a haircut which blitzed the back and sides but left a long lock at the front, which could be tugged out of an edged-backwards steel helmet to show a little individuality while breaking none of the rules.

Both examples from Shots from the Front: The British Soldier 1941-1918 by Richard Holmes, Harper Press, London 2008, (p94 & p173)

No, it's not. For one thing, "long hair" was not really in fashion prior to World War I, and so the length of hair that was generally worn did not change during/after the war years - see this portrait of Hilda, Almina, and Conway Wertheimer by John Singer Sargent in 1905, and compare it to this of Harry Townend by John Macdonald Aiken ca. 1921.

This is a myth that I've heard much more frequently about World War II, actually - that men went to war and got short haircuts, and then when they came back the prevailing fashion reflected the new standard. But likewise, this doesn't seem to be borne out by images of men before and after the conflict. If you compare this Howard Clothes advertisement from 1931 with this L'Homme advertisement from 1951, you again see very little difference in length.

I'm sorry I can't write you a more interesting answer, but there's not much here to work with. It's simply not true.