Stylish retreat for safari-goers near the foot of Mt. Kenya. Why Cottage No. 12 is so much in demand by the celebrity-minded

Peacocks and sarus cranes strut about manicured lawns and lily ponds. Semi-tamed sacred ibises, maribou storks, and Egyptian geese flock to ornamental lakes. In the background rise the jagged 17,000-foot peaks of Mt. Kenya, its tree-covered slopes constantly changing character as sun and clouds move overhead. Most think of it as the hideaway of the late actor William Holden and his hunting friends, and guests often ask to be put up in his favorite cottage - No. 12.

The Mount Kenya Safari Club, originally a mansion known as Mawingo, is a large, two-story white building with balconies and pink-and-white awnings, which would look very much at home in Beverly Hills.

It's rated among the world's top 10 most exclusive clubs and was started in 1959 by a small group of Europeans and Americans, including Mr. Holden and his friends. The club's fame grew, attracting millionaires, royalty, and celebrities as well as tourists arriving daily on safari.

It's an old saying at the Mount Kenya Safari Club that even the insects dress for dinner. Not that you get too many of them at 7,000 feet, but the saying reflects a little of the ambiance surrounding one of the last bastions of the vanishing art of gracious living.

After a daily diet of dusty wildlife safaris and bouncing over potholed roads, culture shock hits you when crossing the club's threshold. In the members' dining room, service is as polished as the silver, and gentlemen must wear jackets, long trousers, and ties after 6 p.m. One visitor wearing a Stetson in the dining room was asked to remove it - or himself.

Once past the club's outwardly snobbish atmosphere, you discover a fine hotel in a magnificent setting with outstanding service and numerous activities.

The main clubhouse faces Mt. Kenya, sharing the same spectacular view with an arc of two-bedroom cottages. The lawn flows down past a heated swimming pool to lakes and ponds where hundreds of exotic ducks make their home. Scattered about 100 acres of lawns and luxuriant foliage are the putting green, bowling green, and an orchid walk. Between the cottages are tennis courts and a nine-hole golf course.

Guests can go horseback riding along 20 miles of bridle path, fish for black bass or rainbow trout, soak in a sauna, or shop in the Safari Boutique for fur handbags, ivory jewelry, batik, and African artifacts.

The club offers a reading and writing room, a conference center and cinema, safari center, piano music in the bar, and barbecues. You can dine in either the Safari Tent grill room or the Hunters dining room, offering six courses of such fare as filet mignon, Dover sole meuni`ere, and smoked salmon.

Lunch can last about two hours while you sample 30 dishes or so prepared by Chef Zickert for the buffet on the terrace. Morning coffee and afternoon tea are served in two spacious lounges where roaring fires ward off mountain chills. Membership plaques line the walls along with autographed photographs of famous members and guests - Winston Churchill, Louis Mountbatten, and the Apollo space crew.

About 130 guests can be accommodated in the club's 78 rooms, each of which has its own log fireplace. Evenings may well be the pleasantest time of day, when a porter appears to light the fire and you can relax while watching the changing colors of dusk on Mt. Kenya and listening to the sounds of birds, crickets, and distant wild animals.

The most popular lodgings are the terraced cottages, all stone and timber. Each has large sliding glass doors opening onto a patio and semiprivate lawns screened by shrubbery, two bedrooms with a spacious sitting room dividing them, and an elegant bathroom with steps leading down to an enormous tub and shower.

In 1967, the club was acquired by Saudi Arabia's Adnan Khashoggi, who gave the club as a gift to his son on his 18th birthday. Unfortunately, Mr. Khashoggi tacked on an ungraceful three-story wing and a few squat garden cottages behind the tennis court. He also erected three large villas that have little in common with the ambiance of a hunting lodge. The rooms and suites in the new Italian-designed villas may well be the most sumptuous in Kenya.

The Mount Kenya Safari Club is too nice a place for a mere overnight stop. The groups of safari-trippers usually troop in late in the afternoon and leave after breakfast, so if you have an aversion to tour groups, they won't be much of an aggravation. On the other hand, the folks on the safari tours bemoan the fact they can't stay longer. On an extended stay, you'll probably share the club with only a handful of guests, except on weekends when members and their families invade the place.

Relax for a few days and watch the sun rise over Mt. Kenya. (Early morning is the best time to see the snowy peaks before the clouds move in.) You can play tennis, swim, golf, or drive up the mountain with a picnic basket packed by the club. The Safari Desk will organize any type of tour - by car, camel, horse, or plane - and will store your luggage while you're away.

Neither the Art or Mountain Lodge is far by road, and Secret Valley, famous for its leopards, operates from Nanyuki, about 10 kilometers (six miles) down the road. Samburu National Park is just over an hour's drive.

If you run out of diversions, you can always do what many of the club's regulars do: just sit around and admire the view. Practical information

The Mount Kenya Safari Club is 120 miles north of Nairobi, 2 hours by car, 45 minutes by small plane. It's open all year and busiest from Aug. 1 through March 31. The period from Dec. 18 through Jan. 4 is reserved for club members only. Daily rates: $84 single, $118 to $168 double with breakfast. Address: PO Box 35, Nanyuki, Kenya. For reservations contact your travel agent.