Really hate the color of my employees hair, and I'm feeling the urge to demand that they change it.
Why do you feel inclined that your obligated to make them change their hair?
I don't think their hair colour goes good with their face.
If the employee likes their hair and it is not against rules, you should leave them alone about it. You cannot control the hair of your employees.
I just don't think it fits her, she could pick up better color.
You're entitled to your own opinion, but you shouldn't force your opinions on other people especially employees. If you try to force her to change her hair you could probably get in trouble with HR.