COVER STORY; Enjoying the splendor of St. Moritz - at prices not strictly for royalty

You could not help noticing the elderly woman. Exquisitely dressed and perfectly coifed, she moved through the luxurious corridors of the vast hotel absolutely at her ease. Everyone, from humble bellboys in dark uniforms to redoubtable head porter - decked out with crossed gold keys on his lapels - knew her.

We happened to meet at the top of the stairs, a flight that descends past the grand piano and the maitre d' into the enormous dining room of the Palace Hotel. I gave her my arm, and we chatted a moment; she slid freely from British-accented English to French and Italian. Thanking me, she proceeded to her usual table, where she almost always chooses to dine alone.

She passes much of the year here, this Principessa. As one of the last survivors of the House of Savoy - which ruled Italy from 1861 until 1946, when the dynasty was removed by a plebiscite - she feels at home in the Palace Hotel of St. Moritz. So did the Dukes of Alba and Windsor. It is that sort of place still.

The Palace is far and away the best-known, although not necessarily the most elegant, of four five-star hotels in this village of 6,000 permanent residents high up in the southeast corner of Switzerland. No other Swiss resort - not Gstaad, not Klosters - boasts so many luxurious hostelries. No other village has twice hosted the Winter Olympics (most recently in 1948), and no other has lent its name to products from lighters to watches.

St. Moritz has catered to the famous and the very rich since the Palace's founder, Johannes Caspar Badrutt, persuaded a party of English Victorian aristocrats to return to his modest inn in winter, then unheard of. He wanted them to try something new - skiing - and come to St. Moritz year round, not just for the usual summer Alpine mountain meadow hiking.

That was in 1864, and his descendants - the brothers Hansjurg and Andrea Badrutt - still own the Palace, running a winter season where wealthy Americans rub shoulders with Arab emirs. They come to St. Moritz because this is the site of the Cresta Run, favored by English aristocrats (headed by Prince Philip) who like roaring down an icy track on mere sleds at 90 miles an hour. The five-star Kulm Hotel, also founded by Caspar Badrutt, houses trophies for the run. Jackets and ties are expected in the public rooms after sunset.

More than any resort in the world - and certainly for more years - St. Moritz is identified with chic. Names like Corvatsch, Corviglia - two of its ski runs - still run through society pages. It is the sort of place where a hotel like the Suvretta House can maintain the highest possible occupancy rate without benefit of public relations, without advertising or toll-free reservation telephone numbers.

Insiders think it is probably the best-run resort hotel in Europe. Terrain on its outskirts provided the choice plots where low-profile industrialists built chalets with bowling alleys, saunas, and indoor pools. Its neighborhood houses the likes of the Aga Khan, Herbert von Karajan, Tina Onassis, and, once, the Shah of Iran.

Chauffeurs from the Suvretta House, clad from cap to toe in olive-green livery, pick up expected guests and their luggage at the train station. They drive away in a matching olive Mercedes station wagon, an understated crest in gold on its door. Naturally, the Suvretta maintains its own ski runs and lifts. With that sort of elan, the hotel need not bother with modern fads like the credit card. The guests are known to the management, they return over many generations, and their checks are acceptable. Such things are still central to the life of St. Moritz.

But what if you are not an international playboy like Gunter Sachs? And not one of that mix of industrial tycoons and European nobility that makes up the 150-or-so members of the highly exclusive Corviglia Ski Club, housed in a deceptively simple, mountaintop aerie? If you do not bring your private 737 into St. Moritz's airport (as some do) but instead arrive by train, taking the fabulous Glacier Express that travels six hours from Zermatt? (It is a slow ''express,'' but the view is well worth the time.) What if your arrival should be by car, or even bus? Does St. Moritz turn a cold shoulder, so to speak, to the un-rich?

Far from it. Without losing the patina of its name, the town offers everything a Rocky Mountain vacation does, and at prices quite as competitive. For example, at the Palace's Chesa Veglia restaurant, the most elegant converted 16th-century farmhouse imaginable, dinner upstairs offers a light fruit sorbet for $6. But $8 will buy an entire ''terrace luncheon'' of several courses, served overlooking the tiny lake where horses tow skiers in a winter race called the ski-kjoring (it came from Sweden).

The four luxury hotels account for only 22 percent of the town's tourist beds; the same views, spotlessness, and reliably excellent service can be had in four-star establishments. They, too, are walking distance from Hanselmann's Cafe , where an official fur, fashion, and jewelry show takes place every afternoon, when ladies gather for hot chocolate and pastry.

The vast majority of the record 30,000 Americans who visited St. Moritz last year found plenty to do, and at prices that do not take the breath away. This summer, thousands are expected to take advantage of an offering by 12 of the four-stars: group rates per person, standard double with breakfast for $25. Half-board (breakfast and dinner) costs only $7.50 more, and three meals a day (so-called ''American plan'') only $15 above the modest room rate. Hotels like the Albana offer essentially the same panoramic look at the mountains as does the Palace. You must decide how much it matters to you that Rex Harrison is staying down the hall. At the peak of last winter's season, top price for a double at the Languard (a garni hotel, serving only breakfast), was $80.

The tourist office, mere steps from the Chesa Veglia, handles without charge reservations for enough flats to add up to 3,000 beds. Their prices depend on size and location, but a medium-level one for four people in winter, fully furnished down to the washing machine, runs $60 to $75 a day. So far, more Europeans than Americans seem to have taken advantage of this value-conscious way to visit in St. Moritz.

Perhaps the most economical accommodation of all is at the youth hostel, open to all (not just ''youth'') with the appropriate membership card in the International Youth Hostels Association. The card is issued through the American Youth Hostels Association, with offices in every major US city. At the height of summer (July and August) preference goes to those 26 and under. The brand-new facility has 200 beds in two- and four-bed rooms and will rent you bedding if toting a sleeping bag is not your style; dinner here is about $3. Democratic to their toes, the Swiss have not hidden the hostel in an undesirable part of town (there is no such thing); it is minutes by bus from the center, as close to everything as is any luxury hotel, or closer.

What about enjoying what St. Moritz has to offer, once you are there? A six-day ski ticket for Corviglia - about 50 miles of the world's finest slopes - costs $65. For $20 more, you have access to a full 200 miles of runs for a week, including ski shuttle bus service. The environs of St. Moritz offer the skier slopes enough for a day's activity without repeating a run. What about the price of a day lift ticket to the top of Corvatsch, where spectacular, red-painted gondolas carry 80 skiers at a time to 10,837 feet? Fourteen dollars in winter, less in summer. The views of rock, ice, and snow alone are worth the price. Such rates compare well with service at St. Moritz's American sister city, Vail, Colo., where a pass of similar scope recently ran $22. Renting skis, poles, and shoes from one shops in town costs about $15 a day.

St. Moritz is ready for you if you do not ski. Skating lessons in the open-air ice rink (the Kunsteisbahn) cost $10 for a 20-minute lesson, with far better rates for a 20-visit subscription. If you bring your skates, adults enter for $1.75, children for $1.25.

When summer comes, winter golf, which had been played on the tiny lakes with red balls (on white ''greens''), gives way to action on Europe's highest and oldest 18-hole course. The lake in front of the Palace Hotel (access to it is not limited to its guests) is host to a 5,000-competitor wind-surfing regatta, and its modest ''yacht club'' is open to all, with a wooden sailboat renting for

Naturally, the Corviglia Tennis Center is not so posh as the private courts in the five-star hotels. But it is new, and its eight clay tennis courts and two squash courts are very efficiently managed. The center, not far from two reasonably priced Club Med hotels and the riding center (which offers reasonable hourly and daily horse rentals), is open seven days a week in summer. One hundred dollars pays for a full summer of tennis, while $3.50 will rent shoes, racket, and balls for a day. You can get a racket for just $1.50, hardly a price only for the rich.

With summer, visitors discover more than the excellent hotel rates. They can find their way to the nearby Swiss National Game Reserve Park (it is Europe's largest). Or they can feed the half-tamed marmots that come out to be fed along the road at the nearby village of Silvaplana.

Fun in St. Moritz, for the price of a bunch of carrots.