SOUTH Dakota, where a sudden blizzard can tip the outcome of a close election, now has taken on unexpected importance with its early-in-the-season Democratic presidential primary.Two Midwestern contenders for the White House, Sen. Tom Harkin of Iowa and Sen. Bob Kerrey of Nebraska, will test their political spurs here - and only one is expected to ride away unscathed. Gov. Bill Clinton of Arkansas, a Southern moderate, also could run strongly in this sparsely populated state where hunting, guns, and taking a poke at Washington are all popular pastimes. "All of a sudden South Dakota has taken on some significance," says Jeff Masten, chairman of the state's Democratic Party. In 1988, he observes, "nobody paid any attention." South Dakota's primary on Feb. 25 follows close on the heels of the first-in-the-nation primary in New Hampshire on Feb. 18. Democrats who ordinarily give South Dakota low billing are expected to wage an all-out fight here for its delegates and the extra media attention a victory would bring. Right now, analysts say Senator Harkin has the edge here - mostly because he got in first. "It's his to lose," says one political insider. But Senator Kerrey is building support. And Governor Clinton is getting organized. What is somewhat surprising is that Clinton is given a solid chance in this primary, at least for a second-place finish, even though South Dakota is widely assumed to be Harkin-Kerrey country. "I don't think Clinton ought to be written off just because Tom Harkin and Bob Kerrey are next door," says Steve Hildebrand, co-director of the South Dakota Democratic Party. "It's a small state and it's not that difficult to get to know people." During the past several years, Clinton has led a nationwide effort to rally conservatives and moderates within the Democratic Party. Mr. Hildebrand thinks there could be a market for some of Clinton's ideas, especially among older South Dakotans. "They would like his courtly approach," says one analyst. Clinton also may do well with teachers, who would appreciate his national leadership on education issues. But the three other major Democrats in the race are not expected to do as well here. They are former Gov. Jerry Brown of California, former Sen. Paul Tsongas of Massachusetts, and Gov. L. Douglas Wilder of Virginia. So far, none of the three have caught fire here. The importance of South Dakota to next year's presidential campaign was unexpected. Ordinarily, the Iowa caucuses, which gave candidates like Jimmy Carter and Gary Hart their starts, take the early spotlight along with New Hampshire. But when Harkin, Iowa's junior senator, got into the presidential race, the Iowa vote became moot: Harkin will certainly win. South Dakota now could take Iowa's place because of its early date and because it will serve as a level playing field in the Midwest upon which Harkin and Kerrey can slug it out for the title of regional champion. A loss here could very well doom the candidacy of one of them. What makes South Dakota particularly tantalizing to all the Democratic candidates is the low cost of running here. Even a political pauper can make a big splash. Candidates can saturate the TV airwaves in every corner of this state in the final two weeks of the campaign for just $35,000 - a mere bagatelle for most candidates. Furthermore, the state Democratic Party provides free mailing lists and services to all qualified candidates, making it possible for a late-starting campaign to blanket the state with literature in the final days of an election without having a large staff of its own. Chairman Masten notes that, for $150,000, a candidate can run an all-out "star wars" campaign here with TV, radio, mailings, offices, and all the other appurtenances one might need. What this means is that someone can come from behind and win here with little advance warning. That's what Rep. Richard Gephardt (D) of Missouri did against Gov. Michael Dukakis (D) of Massachusetts in 1988. With little more than a week to go, Mr. Gephardt came from 16 points back to win by 14 points - a 30-point turnaround in just 10 days. Conversations with a number of analysts here, including political scientist Robert Burns at South Dakota State University and political scientist Alan Clem at the University of South Dakota, yield the following assessments of the six principal contenders here: Harkin. The current front-runner. But Harkin failed to follow up his early lead here, and could be overtaken unless he visits the state more frequently. Kerrey. Most likely to finish second here, but Kerrey has a lot of work to do. He has gained important backing from Ted Muenster, the party's 1990 candidate for the US Senate. Some analysts, such as Dr. Burns, believe that, on primary day, the principal contest will be between Kerrey and Harkin. Clinton. Most of the Dakotans who vote in the primary are liberal, but those who are not may gravitate toward the Arkansas governor. If Harkin and Kerrey evenly split the liberal vote, Clinton could finish a strong third, or even second. Brown. Running an "outsider" campaign against Washington, Brown is expected to arouse some interest. But despite public curiosity, he is not expected to win many votes. Tsongas. "I haven't seen much enthusiasm," says one analyst. Coming from the East could also hurt Tsongas, just as it would Gov. Mario Cuomo of New York if he entered the race. Wilder. Like Tsongas, Wilder looks like a very long shot here. While his moderate views play well in some quarters, they are not expected to make a big splash with Dakota's liberal primary voters.