Three things:
1. If someone grabs your hair, they are currently not punching you in the back of the head with that hand, nor are they choking you with it. Also, you pretty much know where their hand is. I consider all of these things to be good things. I hope somebody pulls my hair when they mean me harm.
2. If someone grabs your hair from behind to off-balance you, just bring your hips in close to them. You will no longer be off balance. They will be in no position to pull you off balance, and you will be in their face with two free hands while they have one. Their hair-grab will be worth nothing and they will abandon it. Better yet, maybe they hang on to it while you mash their face with your two free hands, or pull a double collar tie and show this person how a man grabs hold of somebody. While I'm on this topic, do you have any grappling or muay thai training? That's going to help you understand what I'm getting at here.
3. The one and only thing, in my opinion, that is a pure negative to having long hair is this: a knife. If someone has a knife and they want to stab me with it, my hair is one more handle by which they can get a hold of me, and I'd rather have fewer of those. That being said, having a hold of someone's hair is a pretty loose form of control, and the person whose hair is being grabbed still has a lot of freedom to move around, and I tend to be wearing clothes most of the time, so my hair is usually not the only grab-handle I happen to have attached to me.
I know plenty of competitive fighters with long hair. It doesn't seem to be a problem. If you're worried because you watch World Star videos and see girls get dragged around by their hair, ask yourself why you never see any dudes who seem to have training getting dragged around like that. I'm guessing it's not the disadvantage you seem to think it is. To all the previous posters who said they cut their's off, I can understand that. It takes a moment to tie it back and wash it after you train, maybe that time wasn't worth it for them. I like that my headgear doesn't shift around on my head when I'm sparring because my top-knot sticks through one of the openings and holds it in place.
You can always grow it back if you want to try it and change your mind.