Gleeful President Takes On White Water : Vacation: First Family shoots Snake River rapids in Wyoming. Bill and Chelsea Clinton screech with delight as Hillary sits warily in center of raft.

And now, the White House assures us, the real white water story.

It’s about the boiling rapids of the Snake River here, not the land deal gone sour in the Ozarks. It’s about the First Family enjoying the splendor of the mountain West, which is accessible to millions of American families, not the inside dealing of financial and political speculators in Washington.

President Clinton, First Lady Hillary Rodham Clinton and their daughter, Chelsea, shot the Snake River rapids south of Jackson in the Bridger-Teton National Forest in a 12-person raft for nearly two hours Tuesday afternoon.

The First Family was drenched by the roiling waters of Kahuna rapids, with Clinton and Chelsea paddling like crazy and screeching with glee as their boat was tossed up and down in a stretch of river wild.

Clinton added his straw golfing hat to shorts, a polo shirt and the required orange life vest. Mrs. Clinton was in long-sleeved T-shirt and a white baseball cap in the middle of the raft and looked decidedly warier about the experience than her husband and daughter.

Asked during the trip what he thinks of white water, the President said: “It’s better when you have a paddle.”

He flashed a thumbs-up sign before returning to his lodgings for warm clothes and a cold drink.

The Clintons’ nine-mile river trip came at the end of their first week of two spent exploring the West from Virginia Sen. John D. (Jay) Rockefeller IV’s 7,000-square-foot home at the foot of the majestic Teton Range.

Clinton already has gone horseback riding with Chelsea, hiked around breathtaking Jenny Lake and chowed down chuck wagon style at the touristy Dornan’s outdoor eatery at the edge of Grand Teton National Park in Moose, Wyo.

All of this is designed, at least in part, to try to erase the elitist image projected by his last two summer vacations at Martha’s Vineyard, Mass., where he sang with Carly Simon and yachted with the Kennedy clan.

That the trip is about image as well as recreation is demonstrated by the fact that Clinton is accompanied virtually everywhere he goes by Hollywood producer Mort Engelberg, of “Smokey and the Bandit” fame. Engelberg, who is choreographing every mountain walk and trail ride with an eye toward camera angles, did similar duty during the 1992 campaign and is stockpiling videotape for 1996 campaign advertisements.

“I see this as a forest trail, lined by thousands of well-wishers shouting encouragement,” he said the other day as the Clinton family strolled through a pine forest on the edge of a lake.

What others saw was a large presidential entourage clearing a popular trail to make room for the First Family. Clinton greeted a few park visitors who seemed thrilled by their contact with the leader of the free world; others waited patiently for the group to move on so they could resume their hikes.

Chiefly on this vacation, there has been golf, golf and more golf--at least 131 holes in the past week according to an unofficial tally. On Monday, he teed off with professional golfer and analyst Johnny Miller, a surprise engineered by Mrs. Clinton as a birthday present for the President, who turned 49 last Saturday.

Miller beat Clinton by 20 strokes, with a three-under-par 69.

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Although he promised to lay off the links to spend time outdoors with his wife and daughter, Clinton was at it again Tuesday, playing 18 holes before hitting the river.

In coming days, however, he will have fewer opportunities to play the manicured courses near here. Today he returns to Washington to attend a memorial service for three U.S. diplomats killed in a road accident near Sarajevo in Bosnia-Herzegovina.

He returns here tonight in time to attend a rodeo in Jackson, a little bit of genuine Americana in a resort town that has given way to trendy boutiques and goat-cheese pizza. The rodeo show features the usual calf-roping and bronc-busting, as well as a chance for young children to try to pull ribbons from the tail of a spirited calf.

Friday and Saturday have been reserved for the only substantive business of the Wyoming visit. On Friday, the President will travel by helicopter to adjacent Yellowstone National Park to commemorate the 79th anniversary of the founding of the National Park Service and to hear about the possible environmental damage caused by a proposed gold mining venture on the park’s boundaries.

On Saturday, he and Mrs. Clinton will mark the anniversary of the ratification of the 19th Amendment, which gave women the right to vote. Wyoming, then still a territory, was the first American jurisdiction to allow women’s suffrage, in 1869.

Sometime in the next few days--the White House is being highly secretive about the exact date--the Clintons are expected to camp overnight somewhere in the area.

That is, of course, after the Secret Service has secured the area from possible human or animal threats and the military has laid in the gear to give the President instantaneous global communications.

It will be a true wilderness experience, aides contend, but one unlike that known by any of the 2 million visitors who stream through the area in their campers and minivans each year.