When you think about it snow will not disappear by itself. Depending on the severity of it will depend on how long runways will be closed for. The other factor is visibility. Regardless of technology if it's snowing hard visibility will be reduced and the aircraft will divert. Any carrier will have its hands tied during inclement weather and the detail will be in the planning.
Having said that BA operations have to make the appropriate choice of which flights will go and which will won't. As kazzie says the airport stayed open all day which allowed some movements. Those that arrived and departed were lucky, but there is no guarantee on any flight movements be it short or long haul during bad weather.
Airlines are in the business of making money and not refunding it and BA will do all they can to move passengers to their destination.