Don't know much about BA's operation - would I be right in thinking that the disruption has been overhyped slightly? The airline are only cancelling flights which have several rotations a day. For example, the major hubs in Europe and North America.
And where available, merging flights onto larger aircraft? I very much doubt the load factor would be huge, especially on some routes. I noticed a flight to Frankfurt yesterday was being operated by a B767 - I very much doubt an aircraft of that size would be operating that route in normal circumstances rather than an A320S aircraft. Obviously BA have flexibility in their aircraft unlike other airlines, some aircraft may be utilised when they were originally planned for down days.
Passengers are also given the option to rebook, so that'll free up some space. A lot of extra passengers will be catered for. They've also got their Oneworld and other codeshare partners to "help them out".
Or am I talking rubbish?!
In terms of Heathrow Airport itself, I'd be using this opportunity to lobby the government that cancellations would be mitigated somewhat if extra airport capacity was available! I heard someone on The One Show this evening saying that Munich had 1m of snow alongside the runway and there were no cancellations - they also have same capacity for half the passengers!