I fly SAR in mountains so have some training and experience relevant to this. Helmet fire wrote lots of good information on this. Just want to highlight a few of the relevant points.
Don't hover into the mountain. When you're nose into the mountain you lose references, cut off escape routes, increase your hoist altitude, and may decrease rotor clearance (depends on hoist location).
Small, smooth control inputs. Whenever the rotor disc is tilted from the vertical position more power is required to maintain hover. You may decrease that requirement by gaining forward speed, but initially it increases. If you are hovering in high DA aggressive control inputs may preclude you from maintaining altitude. Try establishing a stable IGE hover and then move the cyclic aggressively-ish. I was able to land a 206 from a 4' hover doing this...center cyclic and you pop back up to the hover.
Cross check instruments. Most of the illusions that are specific to mountains and most that are a result of snow fields can be countered by referring to and trusting in your instruments.
Provide hover references. If the victim is in a uniform field of snow then drop colored smokes, equipment, FOs, whatever you have to create a hover reference. If that just isn't possible, it's probably safer to hover where there are references and have the ground team move the victim.
I'm sure the experience in this group could increase this list, I just included the ones I could think of that I believe may pertain to this incident.
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Regarding the incident, the biggest question I have is why did the helicopter yaw to the right prior to descending? Right yaw occurs only for a few reasons: commanded yaw, application of power, wind and/or tail rotor concerns, autopilot/SAS problems.
After the yaw towards the mountain loss of reference and horizon would be a big concern. If there was an autopilot type problem, then the movements after the yaw may also be uncommanded by the pilots. The apparent aggressive handling (based on the movement of the disc) may explain why the helicopter descended.
The number of scenarios that could explain this are limitless. Right pilot incapacitation (as simple as an impending sneeze) requiring a yaw turn for the left seat to gain reference could be as likely as the autopilot giving away or the tailrotor not providing enough thrust.
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One other thing that was touched on that I'd like to reiterate is for those who have seen the video, what an awesome job the Sikorski did of saving the lives of the crew!!!! Having been to a number of apparently less severe crashes that resulted in immediate fatalities I think that video says a lot for the ~hawk line of helicopters.
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I'm still not sure if this is the same unit that we've visited in the past and they've come to see us for talking turkey and drinking beer. If they are, then I know that they train for this type of flying and have much experience on squadron. Of course, I'd expect most of the units in that area would do appropriate training.
My condolonces to the injured, the families and the unit.