CASPER, WYO., OCT. 25 -- This desolate state, where ranchers live as far as 40 miles from main roads and gamblers play gin rummy because they can't round up enough players for poker, has begun to pose a political difficulty for the presidential campaign of Sen. Albert Gore Jr. (D-Tenn.).

Gore has held that there is no special significance for any of the six states, including Wyoming, that hold primaries before the Southern-dominated "Super Tuesday" on March 8. But Gore is faring so well here that he may want to change his stance.

The Tennessee Democrat took a swing through Casper over the weekend, including a speech to a packed Jefferson-Jackson dinner for the state Democratic Party. He clearly impressed the party faithful. He picked up the support of former governor Ed Herschler, a leader of the party's old guard, and sparked strong interest among younger party activists, many of whom had been openly wary of his stands on contra aid and the reflagging of Kuwaiti ships in the Persian Gulf.

In this conservative state where Democrats oppose gun control and the 1984 presidential bid of Walter F. Mondale was a lead weight on local candidates, Gore struck a deep chord when he said in his speech: "Think what it would be like to have a Democratic nominee for president who could come in and campaign arm and arm with your nominees."

"I was prepared not to be impressed," said State Rep. Pat O'Toole, a prospective candidate for the U.S. Senate. "I was wrong." Leslie Petersen, a Teton County commissioner who is also considering a Senate bid, said Gore's performance "was terribly good." Wyoming Gov. Mike Sullivan (D) said after the speech that Gore "did himself a lot of good here."

This embarrassment of political riches has, however, the potential to throw a monkey wrench into Gore's basic strategy of giving equal weight to the six states holding primaries before March 8.

"I am not setting up any state as a 'make or break' state," Gore said as he prepared to leave Wyoming, adding, "but I recognize the importance of Wyoming."

Wyoming, which holds its caucuses on March 5, is the one pre-Super Tuesday state where moderate-to-conservative Democrats still represent a significant bloc in the party, just the kind of Democrats to whom Gore has been addressing his message in the South.

"If he {Gore} wants to demonstrate that he can appeal to people outside the South, Wyoming seems made for that," said Muffy Moore, chairman of the Wyoming Democratic Party. David Freudenthal, a former party chairman and a key Democratic operative, said, "Gore can come into this state and make the argument, 'I may not be the darling of Iowa, but I can take you to the dance in November.' That can sell here."

While clearly tempted by Wyoming's caucuses, Gore's strategists are unsure whether to make a full-scale effort. In private, they argue that to invest heavily in a state sending just 18 delegates to the national convention would undermine the campaign's basic claim that the existing system of early primaries and caucuses in small states produces weak nominees, and that the first legitimate test of presidential strength will be March 8, when 1,400 delegates will be selected in 20 states.

But the prospect of going for a win in Wyoming is attractive to a campaign that otherwise would have to attempt to retain credibility through March 8 without a victory in any of the first six states.

Of those states, Wyoming is the least organized. No one has made a major dent in the party structure, although most local officials agree that Rep. Richard A. Gephardt (Mo.) has done the most work, winning the endorsements of 1982 Senate candidate Roger McDaniel, State Senator Winn Hinkley and State Rep. Guy Cameron, in Cheyenne -- a key source of Democratic turnout.

The state's caucus system lends itself to campaigns based on direct organizing rather than news media advertising. During the spirited fight between Mondale and Gary Hart in 1984, total caucus turnout was only 3,400 people.

A list of almost all those 1984 voters, plus another 2,000 Democratic activists, is available from the state party, making it possible for a campaign to aim at a small universe of voters, using the mails and phone banks.