Hi A.,
You must have a billion choices from the advice listed here, I wish you the best in approach! I can only answer this honestly as I would have handled it. Children respond well to reward/consequence choices. Use choices but there needs to be limits to his control over you.
First YOU also need to get a trim, even if it is just your bangs or something for show, and your other kids... then, Make a new tradition for life... Offer an ice cream treat or Happy Meal on HAIR CUT DAY on the way home for a reward. Take the reward out of the picture if he chooses to not behave for a haircut... BUT DO remember to reward yourself and your daughter with one. It will work faster than fire on a marshmallow, I'm telling you.
Let him throw his fits, but ignore it and appear to be enjoying your normal day with your daughter or friends who are along. Ignore the negative attention, reward and smile and speak to him when he is not screaming or kicking around. But never raise your own voice. He can learn calm reactions from you.
Enjoy the icecream and Happy Meals!
Your son will soon learn that a haircut means yummy rewards.
P.S.
If you don't stick with whatever plan you set him with, he will worsen and continue learning how to maniplulate. Children are smarter than most people realize, lol.
When he finally does the right thing... give him a million smiles, hugs and applause.
=)