The snow on the Wasatch Mountains loomed thick in the east, but the citizens of Salt Lake City stepped back today from the worst flooding in recorded Utah history to enjoy their new place as the Venice of the high desert.

Swamped by torrential mountain runoffs that sent sewer manholes spouting 15 feet into the air and buried suburban neighborhoods in mud, the largely Mormon population of this usually bone-dry city has created an instant network of street canals, waterway bridges and dikes. With them have come an almost carnival atmosphere to this tidy and somewhat austere state capital.

"I have some friends who say they are going to get a power boat and do some water skiing on 13th Street South," said Utah Cattlemen's Association executive vice president Michael Sibbett, joining a crowd of amateur photographers lining the makeshift canal that was once State Street.

"I like it," said Darrald Bradley, 15, who is visiting with his family from southern Utah. "It is not every day you get to see a river running down a main road."

Today the crowds were even larger, with ice cream vendors and tourists joining the crowds of city residents out to admire the product of their week of frantic midnight sandbagging.

The final touch to the Venetian scene, two dirt and asphalt bridges arching gracefully over a bank of steel conduits on the State Street canal, were built in less than 24 hours to handle today's rush hour.

Traffic proceeded with few problems, but people out to admire the canals and bridges eyed the snowcapped mountains to the east with suspicion and remarked to each other that the weather seemed to be getting dangerously warm again.

A freakish worldwide weather pattern has left much of the western United States soaked to the core and facing a possible rash of summer flooding. In Utah the rapid runoff from record mountain snow packs--a total of 805 inches of snow fell at the Alta ski resort--has already taken three lives, forced at least 3,000 temporary evacuations and turned 13 of the state's 29 counties into disaster areas.

Gov. Scott M. Matheson has estimated cleanup costs at $200 million. Although the flooding abated this weekend as cooler temperatures slowed the snow melt and some parts of the city's makeshift canal system even went dry, officials still predicted more crises to come.

"It depends on the warming trend," said Salt Lake County flood director Terry Holzworth. Temperatures were in the mid-70s today but officials feared a return to a 90-degree hot spell that sent water and mud cascading down mountainsides a week ago.

Holzworth has predicted "the worst flooding in history for the next three weeks on Big and Little Cottonwood and Mill creeks," which carry water from the eastern mountains to the Great Salt Lake and the Jordan River on the city's western edge.

Jim Bridger, the famous 19th century mountain man, once told Mormon leader Brigham Young that settling this arid plateau would be impossible. But Young and the other pioneers of the Church of Jesus Christ of Latter-day Saints discovered that close community cooperation could harness the mountain runoff and make this desert bloom.

Today water sprinklers incongruously wet the bright green grasses near the city airport and city streets soaked up the shade from huge maple trees, while the descendants of those Mormon pioneers put to use that system of community service to build up the sandbags around the next flooding threat.

More than 14,000 volunteers have worked in the last two weeks to arrest the flooding and clean up the neighborhoods in Farmington and Bountiful to the north, where flooding and mud slides have been particularly severe.

The first danger signs here came late last year, when the 1982 rainfall reached 25.15 inches, 10 inches above average. Cool, cloudy weather so reduced evaporation from the Great Salt Lake that it made its highest seasonable rise in recorded history, inundating roadsides and parks.

Mountain mud slides began, the worst an April 18 disaster 50 miles south of here that plugged Spanish Fork Canyon, drowned the small town of Thistle and cut the main highway and railroad lines for what may be months.

When the record mountain runoff hit the city itself in late May, the Mormon church organization, which claims about 70 percent of the state's population as members, put into effect longstanding emergency plans.

Sibbett said 300 volunteers from his and other local wards of the church were called out within 20 minutes at 1 a.m. Memorial Day. Water was shooting up in 15-foot geysers from the storm sewers under North Temple Street. Sibbett and others filled sandbags throughout the early morning to create a new street canal there.

Neil Stack, county flood control operations coordinator, said more volunteers today completed a new mile-long street canal on Pheasant Way in the southeastern suburbs, where the next flooding threat is anticipated.

In the northern downtown section, bisected by State Street, which runs a block past the spires of the Mormon temple, the water was down to about two feet. Mothers felt it safe enough to prop their children against the sandbags for pictures.

Once the waters recede completely, the streets will be a mass of potholes, carpenter Dan Royal said glumly. He had often ridden his 1968 GTO convertible on the main thoroughfare but, he said, "Nobody is going to be dragging on State Street anymore."