I think that would be a temporary treatment, because as soon as the cold is removed, we'd have heat rushing to the head again. Also, cold area's would result in less blood flow. Less blood flow means less nutrients being supplied to hair. I've heard that DHT travels in blood?, I'm not sure if this is true but even so, what's the difference between starving your hair of food, or poisoning it?
Another reason why it wouldn't work: You'd have brain damage before you have temperatures cold enough to induce hair growth. I'd rather be able to speak than have a full head of hair.
All that aside, in my most desperate hours, I have tried putting ice packs on my head. Didn't really lead to anything though. It was a really hot day, and I thought, might as well cool myself down and see if this does anything.