On one level this is complicated situation, but on another level it's incredibly straightforward.
Having got into the position of having crowds of people camping out in the airport a fair bit of goodwill could be reclaimed by treating them to a bit of hospitality - unlimited food and (non alcoholic)drink should be a basic I would have thought.
Undoubtedly some frustrated passengers make things difficult - one of my daughters worked at the airport for a couple of years, and some of the things she experienced passengers doing told the other side of the story. Nevertheless, it's Christmas, and the level of tension is going to be high. The airport operator isn't to blame for the bad weather, but to a large extent it is responsible for what appears to be an almost total collapse of organisation in terms of dealing with the consequences.
The airport operator doesn't schedule flights, and doesn't cancel them - it's worth remembering that the airlines do all that. The airport operator's job is to run the airport, and that includes operating around and through bad weather. If say, Canadian airports came to a virtual standstill because of 150mm of snow they would be out of action for six months a year. I've taken off from and landed on American airports that had five times as much snow each side of the runway, but things went smoothly.
Heathrow is in trouble because of a failure to invest enough in snow clearance technology. No doubt we'll hear the 'lessons have been learnt' mantra being chanted after this is over, but it isn't enough. We've heard all that several times before, and nothing was done. It's time some people resigned and let others make a professional job of it. If something isn't done, and done quickly we'll lose billions of valuable airline business to other European airports.