I have to say that the bulleted answer that I just read was incredible, and a lot can be taken away from that to understand the Saiyan race.
In my eyes, the Saiyan's hair is a very key part of their ki control, their physical stature, and their own understanding of themselves. I believe it was Vegeta who said to Bulma that a Saiyan's hair never grows, it never changes (to paraphrase, of course).
Saiyan's hairstyles and strengths
It does not seem that the length of a Saiyan's hair is immediately related to the base power of the Saiyan. The Saiyan saga made it quite clear that Raditz is weaker than Nappa is weaker than Vegeta, and the lengths of hair do not grow shorter or longer in that sequence, as Nappa is bald and is stronger than Raditz (according to Team Four Star, Nappa is 5Raditz, lol). It's possible that I'm wrong, and Raditz had unrealized potential to be unrelentingly strong but was too mentally weak to achieve it. However, I don't believe this to be the case.
Supers and their hair
Now onto the relationship between the hairstyle and Super Saiyan abilities. To make a note, all the Saiyans we know to have achieved a true Super Saiyan form, had hair. This is minor, but makes the analysis a whole lot easier. Goku and Bardock were the first two Saiyans in known history to transform and they had the same fairly short, spiky hairstyle. Vegeta's early SS form was a bit invalid in my opinion, as he forced his way in, like achieving full meditation with help from drugs. However, his hairstyle is in many ways very similar to Goku's, which I will comment on in my next point. Goten, same hairstyle as Bardock and Goku, and as far as Trunks, that's just a different story, I'll make a side point in the end for that.
Goku vs. Vegeta
So what is the difference between Goku's hairstyle and Vegeta's (in base form)? If you look closely, their hairs are actually quite identical. I've never counted the spikes, however. If Goku's hair was forced upward I feel that they would be the same length and style. This opens up to my real idea of what the hair represents. On Earth, martial artists have the ability to suppress their power, not hide, but suppress. Vegeta learns this, proving he never had this ability before coming to Earth. So while Goku spent his life only bursting his power at the moment he needs it, Vegeta has always pushed himself to the limits at all time. I believe their hairstyles resemble this. Goku is always at peace and relaxed, so I believe his hair is relaxed and does not flow as much ki. When Goku uses the Kaio-ken, his hair rushes up for just a moment.
A channel for ki
So all in all, my theory is that a Saiyan's hair has no cosmetic value, and is a direct representation of their average ki consumption. When Goku and Vegeta transform, their hair is passing far more ki than normal, and this causes it to stand up and resemble their aura. For all known Super Saiyans, there is a gold aura, however we do not know that this is always the case. Perhaps the SS of legends, thousands of years ago, had a green or red aura. However, Goku and Bardock have a golden spirit aura and Vegeta learned to transform by watching Goku, resembling his technique and passing it to his son Trunks (again, not getting into that little bastard). Broly's final transformation had more of a green aura as well, but I'm not an expert on the movies.
The typical first transformation involves the hair turning from black to gold, and the eyes turning bluish-green. The next transformation involves the hair to flow even more forcefully upward, the aura to grow sometimes with lightning, and muscle growth. Then the transformation to SSJ3, which I have only seen done by Goku in the greatest scene ever, involves the obvious growth of hair, more muscle growth, and some major facial changes.
Now I think I'll get to my opinion on the question that was asked. In the SSJ3 form, not only do the eyebrows disappear, but the entire forehead grows severely. It seems to me that the top of the head and base of the hair is the last biological point in the body which passes ki, and the growth of his cranium is no doubt to accommodate the intense flow of ki. The eyebrows may serve as an auxiliary port for key to enhance vision and the senses, or even just to project ki in different directions. However, when the body must focus enough energy to reach such a high level, such accessories are pointless, therefore they vanish into the flow of ki. When I watch Goku transform for the first time on Earth, I see him not only intensify his own energy, but taking it in from the world, like a slowly expanding spirit bomb in a way. The clouds fly towards him, the grasses bend his way and all the trees shake immensely. His body is at that point holding far too much energy to handle and he must adapt his physical body to survive and use that energy. This is where the hair reacts and becomes much larger to allow him to hold the energy a little longer and direct his power much more finely. This doesn't answer the question how hair could just grow and shrink, but the idea is, maybe instead of calcium and proteins, a Saiyan's hair is made of raw ki.
I promised to make a side note on how Trunks' hair works, so here it is. Trunks can go screw because I don't want to think about the one hole in my entire theory. Bulma is ruining it YET AGAIN and I'm sick of her s**t. SICK OF IT!