Sometimes, after 12 years of ice shows, television, Las Vegas, as Peggy Fleming cuts figures across the ice, sometimes the thrill surges up again.

"Sometimes if I feel real cute," she said with a hint of a playful smile, "if I feel confident and thin and pretty and I know the choreography really well and I'm in a good mood and everything's clicking -- everything's right -- that's when it's really good. It doesn't happen very often."

It happened last week at the Capital Centre, she said, when she skated to Jane Olivor's "Some Enchanted Evening."

But yesterday afternoon, no doubt, she was too cold to tell if it was happening. She had been dreading the weather. Still, as the 34-degree air settled over the South Lawn of the White House, Fleming skated out onto a portable ice rink, 20 by 30 feet ("a postage stamp," said her manager Lee Mimms), to the same song, wearing a filmy chiffon halter dress, glittery silver straps criss-crossing her bare back.

"Poor baby, she must be freezing," said Mimms, in a fur coat as he watched her bow to the crowd, one knee on the ice.

The president was giving a party on behalf of the Secret Service agents and military officers who work at the White House. Fleming's performance was the highlight of the ice show for the crowd of more than 1,000 -- White House staffers and friends -- who sat on folding chairs, bundled up against the cold. "We had anticipated having a warm day," President Carter told the group. "But Pat Caddell's survey was not exactly accurate." This elicited weak laughter.

"You have performed like true Olympians," Carter told the audience. "To show you, we have an Olympian here . . ." he said, introducing Peggy Fleming before taking his seat between Rosalynn Carter and Fleming's husband of 10 years, Greg Jenkins, a dermatologist, who held their 3-year-old son, Andrew.

Fleming skated three times for the crowd yesterday during the mid-afternoon party -- the first time in a beige leotard with purple fringe. With a sweep of the arm, she glided across the ice, propelling herself into a camel spin, fringe trailing, her face serene. Suddenly it might have been 70 degrees. The chilled audience sat so quietly that only the scrape of the blade was heard. Fleming skated again for a performance at 6:30 p.m. at a Christmas party for White House staff.

In the 12 years since she won the Olympics, she's never stopped skating across some ice somewhere.She's done TV specials. She's done commentary for network sports. She's done a guest appearance on the TV show, "Fantasy Island," (skating of course.) And in ice shows, she's skated Vegas and Tahoe and the Peoples Republic of China.

She squirmed in the Las Vegas atmosphere ("I didn't feel comfortable"), and stayed in her room when she wasn't performing. But she loves Lake Tahoe. "It's gorgeous. People go there to backpack and ski. They're not just there to gamble. Everytime I've gone there I've been the headliner. [The hotel] gives you a Rolls Royce and you get waited on. And a man takes your guests backstage and you can serve them drinks."

She's skated for Trident sugarless gum on television and she'll skate for L'Eggs pantyhose soon. She's skated at small rinks and big rinks and six months pregnant. (They just let the costumes out.) She's skated at her friends' skating parties. And even though she opposed Carter's boycott to the Summer Olympics in Moscow this summer, she skated at the White House in freezing weather yesterday.

At 32, she says she's still not bored with it. "I always try to improve -- each year," she said. "I do something new -- a little more creative. I've been doing some commentary for CBS. I've done just about everything in skating. But you can try something just a little different -- no big turnarounds in style."

She still gets a little nervous on the ice -- but nothing like the Olympics, where her whole life passed before her eyes. "My nightmare is that they'll call my number," she said, "and I won't be ready. I'm always a little late."

She travels a lot doing television and skating. This time, she brought her child from their home in Los Gatos, Calif., so that he could see the White House. Her husband travels often with her.

"If I get depressed I talk to him," she said, "or I talk to my friends."

Dorothy Hamill -- the 1976 Olympic gold medal winner who was also on the ice-show circuit for a while -- had spoken of her post-Olympic letdown. "It must have been hard on Dorothy," said Fleming. "We all went through the same thing, I don't know her very well. I just think when you get depressed, you should talk about it with your friends -- not with the press."

Fleming is striking now -- on the ice and close up -- more sophisticated than the 19-year-old who won the gold medal at the 1968 Winter Olympics Exotic, with her gray almond-shaped eyes and her long brown hair crimped with waves. A couple of years ago she had her nose fixed.

"It was much longer," she said, grinning and running her finger along the bridge of her nose. "I had been seeing photos of myself, thinking 'I hate it, I hate it.' When I turned 30, I thought, 'Okay, I'm grown up. I can make big decisions for myself. No one else can tell me what to do. If this bothers me, I'm going to fix it.'"

She has lost a lot of the ice-princess demeanor that she displayed at Grenoble, France, in 1968 when she won the gold medal and the Star Spangled Banner was played for her -- the only American athlete for whom it was played that winter. Immortalized, via satellite, in chartreuse, thick hair piled up: Peggy Fleming, "ice ballerina," "dazzling ice queen."

And what an ice queen: At press conferences she said young people needed people to look up to and she pronounced sports figures like Joe Namath "a mess." Hippies, she said, were trying to "just feel in."

Sunday, reminded of that incident, she nodded as she sat in her suite at the Springfield Hilton, where she will perform tonight with the "Hilton on Ice" show. "I guess I was pretty straight. I was 19 years old. I looked up to people. I thought, 'Hey, now, people are going to look up to me. I have to set an example.'"

She began to loosen up, she said, when "my husband and I went through a period in San Francisco for five years when he was an intern, where we were into being more groovy, seeing show, doing things like that."

After she won the gold medal, her mother proclaimed that she wouldn't be getting into all those ice shows. "Well, I did wait," she said Sunday. "I did a television special first. That's why I got the contract with Bob Banner [a television producer]. I wanted to be surrounded by people I liked."

But eventually there were the ice shows -- and the money. And the schedule in which day becomes night becomes ice. Off and on for 10 years in 26-week tours (other ice-show regulars skate 44 weeks). "You close the show Sunday night and pack all your clothes and then get on a plane to go to the next city," she said. "Then the next morning, you have a press conference and you have to be nice and cheerful and then get into your costume and skate. Sometimes I felt sorry for myself. But you can't feel you're the only person in the world who skates."

So, she says, she did the ice shows but she did them her way. "That whole concept of doing only 26 weeks was started by me. No one else had the guts to ask for it. Then Dorothy [Hamill] stepped into all that and she had an example to follow."

Through it all, she has protected herself: from the press, from the pressure. On the day before she began her school figures at the '68 Olympics -- where "my life passed before my eyes" -- she didn't march in the opening ceremonies. "It was too cold," she said. "I couldn't see jeopardizing my chances for a gold medal just to march in the opening ceremonies. I watched it on TV."

Of this year's silver medalist, Linda Fratianne, Fleming said, "I thought she did well, considering the pressure. They were probably on her a little too much -- it probably broke her concentration. There's enough pressure without having to think about reporters asking you, 'How are you feeling? How are you doing? What are you eating?' I know everyone has their job to do, but her concentration should have been just on her skating."

Fleming has no definite long-range plans, but her Ice Follies days are past. "I've done the ice-show scene," she said matter-of-factly. "I did it 12 years. It gets run-of-the-mill."

She still does ice shows -- but they are her shows or just guest appearances. And she has no idea what she'll do after no one wants her to do any more shows or Trident gum commercials. "I guess I'll always have a foot in the door," she said.