As an American living and skiing in Europe now, I'll offer a few observations that I've made over the last few years which might explain the differences.
First, a lot of European countries have a week-long school break in late January or February, similar to spring break in the US. Since it's winter instead of spring, a lot of people with kids use the time off to go skiing instead of going to the beach. Also, Europeans tend to have more vacation time in general, which means they can take a week off around Christmas/New Years and then another week a month or so later and still have days available in the summer to do typical summer trips. So, they don't have that either/or decision to make about winter or summer vacation; they can do both.
Second, destination ski trips are much more affordable and convenient in Europe than they are in the US. To begin with, lift tickets are much cheaper. For example, if you go to one of the big resorts in Austria or France, such as St. Anton or Val d'Isere, you'll be paying about $50-55 per day, and that doesn't involve hunting around online or going to random shops 10 miles down the road that offer discount tickets; that's the walk-up price. One of the reasons for those lower prices is the larger size of the ski areas. The larger size means people spend the whole week in one place, which allows them to get multi-day discounts on 5- or 6-day lift tickets, rather than buying a bunch of single-day tickets to different resorts.
That larger size also makes things more convenient. If you're in a ski area that has more than enough terrain to keep everyone happy for a week, then you don't have to go resort hopping. And since most areas sprouted up from existing towns, there are usually enough shops, bars, and restaurants to keep people happy in the evenings as well as enough accommodation for most visitors to stay at the base of the mountain. That all makes accommodation easier to sort, and it means that you don't need to rent a car if you've flown in. Once you get to the resort, you're set.
It also makes package trips easier to set up for travel agencies, since they can charter flights and arrange their own transfers on large buses to get their customers to and from the resorts. So, you can book a package where someone else has already sorted the details for you and can take care of things on your behalf if you get delayed/cancelled flights or any other mishaps. And just to add to the convenience factor, for those wanting to do it all themselves but aren't within driving distance, there are several budget airlines with point-to-point flights to Geneva, Zurich, Grenoble, Turin, Milan, Venice, Innsbruck, and Salzburg.
As for the question about what could be done to increase participation rates, my answer would be to make it cheaper and easier for beginners to get started in the sport. Here in Britain, it's quite easy for a never-ever to get started, which is one of the reasons why the UK has a 10% participation rate despite only having a couple of small resorts in Scotland and being such a long distance from the Alps and Pyrenees.
Edited by CerebralVortex - 4/7/16 at 5:35am