Well here is a twist on this question ... can a referee wear a helmet if they want to? Or for that matter other equipment that may be dangerous to another? How about hats or long pants?
The answer dear friends, is no. And it's even in the LOTG.
First, take a look at my previous post of "What's a snood, and why is FIFA banning them?" Pretty straight forward, yes?
Now, please take a look at "Snood, You Lose", from HK Referee, and we are treated to pictures of FIFA referees, yes FIFA referees, wearing snoods.
Now, besides the fact that they look silly on a referee, why not wear them if practical you may ask?
Well first, it immediately sets up a "do as I say, not as I do" paradox between the players and referee. After all, why shouldn't the referee follow the LOTG as well? After all, they are responsible for enforcing them.
A better answer is actually in the LOTG itself. Take a look at the interpretation section which states:
"Referees are also prohibited from wearing jewelry (except for a watch or similar device for timing the match)."
Why would that be you ask? Likely to protect players from harm in a collision with a referee. So here, not only would jewelry apply, but also a dangerous item like a snood.
I would opine that the same applies to the dress and appearance of a referee. It would seem hypocritical to have it any other way. HK Referee and I agree on this one.
After all, we are there to enforce the laws by example first, and action as needed, second.