It is absolutely a case for EU compensation then it seems to me, I can understand perhaps BA being unable to reaccomodate a whole aircraft worth of PAX over to UA although I would suspect some of the higher rev PAX received this offer. Read through the threads here on EU compensation to get an idea of what you are entitled to, this should be the main focus of your claim, although perhaps you might tack on a claim for any clothing or equipment hired to enjoy your ski holiday, I have experience of NW actually paying up for a similar claim where they lost skis into DEN for several days and with OS for boots that decided to travel via AMS for reasons best known to them.

Once you have assessed the amount of your claim submit a letter recorded delivery allowing them 14 days to respond with a cheque (this is rather generous since they are technically only allowed 7 days), after which time you will file a claim in the small claims court. After the 14 days are up go to moneyclaimonline and file your summons. This is probably the quickest and easiest way to get to what you want. I would hazard a guess that there is perhaps at most a 5% chance of BA paying up without being sued, but you have a reasonably good claim (which would appear watertight in the absence of any hard info on why the service to DEN was cancelled, hopefully someone here might be able to help you with that).