I can't answer the compensation part of it as it appears to be a little up in the air based on what legally qualified people have said, and neither have I ever claimed it so I cannot even offer you an answer based on my own experience.

However, BA have never quibbled over refunding my hotel costs when I was disrupted (and many of them as I am a disruption magnet - the snow, the fog, all sorts), even when it was due to weather and completely beyond BA's control. You'll need to write in with all the receipts and they will refund it - it may not happen very quickly, but they will refund it. Usually during mass weather-related disruptions there was a limit of £200 per person and they informed people in advance of it, but I am not sure if this applies to you.