martyg, what is your affiliation with this?
Most of the "case studies" I read through their website, including those with TRX and USA Cycling, are actually press releases. Other "case studies" such as with UNC suffer from selection bias: These are groups that have radically transformed their training programs, so no results can be reliably attributed to this tool.
Research into the underlying technology, transcranial direct-current stimulation (TDCS), seems to show mixed results, with either no discernible effect or very slight improvement to cognitive tasks. And while there's a cognitive piece to skiing, I'd argue most seasoned non-racers have the cognitive (decision-making) part dialed in. It appears in my quick google search that studies have not been run extensively to verify the effectiveness of TDCS in psychomotor development*.
More importantly, since halo is a private company, there's no way to know if their implementation is simply flim-flammery and snake oil. And based on the stretched truth, reliance on technobabble, and hyperbolic claims on their website, I'm certainly not buying what they're selling.
My suggestion to people who want to improve is to train smarter. Work with your coach to establish goals and challenges. Do video analysis to understand your areas of opportunity. Review good media, like Total Skiing, Ultimate Skiing, the Projected Productions videos, etc. Train in the gym to develop your range of motion, strength, explosive power and endurance. Work with a sports psychologist to discover the barriers you have and move through them. Get well fitted boots and appropriate skis, and maintain them throughout the season. Review with your coaches and get feedback regularly in all these areas. Repeat.
I would bet my retirement savings that this type of approach will give better results than using these expensive tingly headphones. And while you could do both, certainly to me it seems foolish right now to spend $750 on this product. That money would likely be better spent on a season pass, or a good slalom ski, or intuition liners and boots, or lessons, or extra days on snow.
*In cases of depression, it appears that TDCS helped develop psychomotor skills. So if you're depressed and don't intend to treat depression (or treatment fails), one could hypothesize that you would improve your turns with a TDCS system. But again, that would be an untested hypothesis - and I'd suggest in such cases you probably have bigger things to worry about than your skiing performance! If you're depressed, get out on the slopes on a sunny day; soak up some vitamin D, breathe that clean mountain air and get your heart rate up. Exercise has been shown to reduce depression.