Each year American travelers make the same old mistake. They go to Europe in the summer. They go at the peak of the season, sprawling across the continent in search of the big-city sights and big-name resorts -- the same hot spots everyone else wants to visit at the same time.

Once there, what they get are not only the charms and ambience of Europe, but a chance to spend most of their waking hours competing with other tourists. What they see are not only the sights, but many of their next door neighbors, about half the population of Ohio, nobody knows how many Germans, and, of course, most of Tokyo. Result: Too often the treasures of this great travel destination are lost in the crush.

That's why the best time to go the Europe is now, before winter ends. That's right, winter. The same bone-crushing winter that stood Napoleon on his head in Russia. The same damp, drizzling winter that gave Julius Caesar head colds and cattarrh in Britain. The same brutal, snow-choked winter that froze the tears on the cheeks of Hitler's troops.

But also the same soft, powdery winter that brings us the Royal Ballet in Copenhagen, the symphonic orchestras of Stockholm and Vienna, the opera houses of Paris and Rome, the concert halls of Poland, the Great Alpine ski centers, the London show tour, museums and galleries uncluttered by other tourists, and a Mediterranean coast that is warm and uncrowded.

Nor is it necessary in most places to dress as if heading for the Yukon gold fields. True, there are places in Scandinavia where, in the winter, even a polar bear wouldn't go outdoors without a scarf. But that's not so true of the greatest city of the region -- Copenhagen -- which glows brightly during the gray, drizzly months, its cafes, concert halls, theaters and cabarets in full swing.

This is the real Copenhagen, not the Copenhagen of summer. This is the Copenhagen of swirling snow storms, bundled babies, early twilight and late dawn, beautiful women in fox coats, men with pipe smoke swirling around their fur hats like clouds.

For a visitor, it is the time for the arts. The Royal Danish Ballet is perhaps Western Europe's finest, presenting classics and innovative programs in the 200-year-old Royal Theater from September through May. The theater, shining like a welcoming cultural beacon on a dark winter's night, also houses the country's fine opera and drama companies and visiting artists. The highest priced ticket for the ballet is only $10, a bargain in this land of high prices.

And that's another nice thing about winter in Copenhagen and the rest of Europe -- the prices come down. Most Copenhagen hotels offer rooms at prices at least 20 percent lower than the peak tourist month prices. Some, such as the Scandinavia, even have half-price rates after 5 p.m., so it's sometimes wise to delay checking in until after 5 if you don't have a reservation.

The Danish Tourist Office, in its effort to lure more tourists to the city in the off-season, issues a "Winterful Copenhagen" coupon booklet valid Oct. 1 through April 30. In addition to its use as a mini-guide to the city's attractions, the booklet gives you 16 coupons, good for everything from a 50-percent discount on admission to the Mechanical Music Museum (don't miss it) to special prices at restaurants such as the Restaurant Felix in the Sheraton-Copenhagen and the Anva Restaurant on the Vesterbrogade.