Skiing is a much more expensive activity in most of Britain, mainly since it requires taking a week off work, international flights and hotels to be able to participate. And to become good at skiing you'll have to do that once or twice a year for many years. In places where the local ski slope is a bus ride away it is much less of a class/wealth thing.

The height of ski chic in Scotland used to, at least when I skied regularly, consist of offshore foul weather gear emblazoned with the name of the oil company (or oil service company) the wearer had borrowed it from.

Exactly! I used to ski double black diamonds in the Sierra Nevada range wearing jeans, with gaiters to keep the snow out of my boots.