In reply to nickinscottishmountains:
As far as I can tell, generally when I am skiing I wear a hat to keep my head warm when it has cold air going past it at 30mph, and ski helmets have lots of warming foam inside them to do the same job. I dont use a ski helmet but I am told they are nice and snug.
When I trad climb, I wear a helmet and it doesnt have any foam/insulation yet more times than not my head is still dripping with sweat after a long trad pitch. I also have a cycle helmet and it is bulkier than my trad climbing helmet which I already manage to knock all the time, so I dont think my cycle helmet would be very good for climbing.
So climbing, cycling and skiing are all different and have different requirements of a helmet. So the optimum helmet for each would be different, that said wearing an un-optimal helmet would probably be better than nothing against some incidents, so you could wear the same helmet for all three it just wouldnt be as comfortable or provide the same level of safety.
For what its worth, I wear a lid trad climbing (falling rocks/unpredictable lobs) and cycling (scared of getting hit by a car), but dont for sport climbing/bouldering (smaller more predictable lobs) or skiing (started 24 years ago before they were invented, and dont fall all that much).