Als Skischaukel bezeichnet man die Verbindung von in verschiedenen Tälern gelegenen Skigebieten über die Höhenzüge, die diese Täler trennen. Dadurch können Skigebiete beachtlicher Größen entstehen, z.B. die Trois Vallées in Frankreich.
http://de.wikipedia.org/wiki/Skischaukel

Skischaukel and Skiarena are terms typically used in Germany and Austria. I can only speak for the US, so I'm not sure how the Brits would call it, but you wouldn't find expressions such as "ski arena" anywhere in the US. It's just called a ski area, ski resort, or ski terrain.

One lift ticket to 4 mountains: Snowmass, Buttermilk, Aspen, Aspen Highlands. Located in the heart of the Colorado Rockies, approximately 200 miles west of Denver and 10 miles from Aspen, Snowmass is one of the largest and finest ski areas in North America. Eighteen lifts provide access to over 3,000 acres of ski terrain, with a capacity of over 24,000 skiers per hour.
http://www.otol.uic.edu/snowmass/index.htm

While Breckenridge Ski Resort is home to 4 mountains and 2043 acres of some of the best skiing in the world, Keystone, Copper Mountain, Vail, Beaver Creek, and the legendary Arapahoe Basin are all within a 40 mile radius from town.
http://www.breckenridgelodging.us/breckenridge_skiing.html

Lutsen Mountains consists of four separate mountains spread over more than 1,000 acres of forest. The ski area's 87 runs offer variety and challenge for all abilities.
http://www.skisite.com/downhillDetail.cfm?id=444