The road toward Bjelasnica Mountain, where much of the 1984 Winter Olympics will take place, was a villagers' path until last year. Sheep in the area still tend to behave as if the new pavement has been laid for them, occasionally meandering in the way of visitors coming here for a pre-Olympics look.

"It adds to the atmosphere, you see," said Pavel Lukac, Sarajevo's public relations professional, marking time as a passing herd of matted mountain animals forced his car to a stop the other day.

Convincing the world that Yugoslavia could shed its woolly image and be host to the Winter Olympics hasn't been easy. But it's getting easier as this central Yugoslav city begins to wake up to the idea of itself as a future center of world winter sports competition.

Set in stunning Alpine forests, Sarajevo's recently completed Olympic slopes, ski jumps and bobsled track look from a distance like the first brush strokes on a wilderness canvas. Downtown, the freshly cast Zetra Olympic Hall stands off against a 600-year-old Moslem bazaar and tall rows of worn tenements strung with clotheslines.

The feel of the place is socialist working class, which is not exactly in league with the quaint touches and sophisticated charm of such past Olympic locales as Chamonix and St. Moritz. But that's part of the point.

As the first so-called developing country to act as host to the Winter Games since they began 59 years ago, Yugoslavia will represent a political milestone when the Olympic torch is lighted here Feb. 7, 1984.

Maneuvering around this Balkan nation's economic troubles--which include a $19 billion debt to the West, shortages of essential goods and high inflation--it took a world-class effort to finish the Olympic complex in time this winter to be host to 10 international sports events. These pre-Olympic trial runs came off with remarkably few hitches.

Remarkable, that is, to those skeptics--and there were more than a few in 1978 when the 1984 Olympic contract was awarded--who regarded Yugoslavia as a risky choice. The country is better known for its summertime Adriatic coastline than its wintertime mountain skiing.

Moreover, the Olympics bid went to the more primitive central Yugoslav republic of Bosnia-Hercegovina, rather than to the northern, more developed republic of Slovenia--which hadn't bothered to try for the Games given the odds against any Yugoslav state winning.

"People had been joking about having an Olympics here for years," said Lukac. "Then someone at the OEDC (Organization for Economic Development and Cooperation) in Paris did a study showing that the terrain here is excellent for the development of winter sports.

"That fact," said Lukac, "together with your usual Yugoslav enthusiasm, encouraged us to put up a bid. After we won, we drank, got sober then realized what we'd done."

For a long time afterward, many Yugoslavs, watching their country's economic problems mount, looked on the enormous cost of being Olympic host as a foolhardy extravagance. According to Branko Mikulic, president of the Sarajevo Olympics Organizing Committee, the 1984 Games will cost an estimated $163 million. This includes $103 million for sports facilities and $60 million for equipment and organization.

But local officials are confident they will clear the financial hurdle, thanks in large part to the $91.5 million that ABC is paying for exclusive U.S. television rights to the Games (Sarajevo gets $66 million of this, the International Olympic Committee gets the rest), plus undisclosed sums being paid by networks from Canada, Japan, Mexico and Europe.

Corporate sponsors and licensees are also contributing substantial amounts. Lukac wouldn't provide any particulars but he did say that the hotly competitive company bids for the Olympics rights far exceeded initial estimates by the organizers.

Among the standard big names on the corporate contributors' list is one less conventional standout: Ooh La La Inc. of Monterey, Calif., providing pins for both the Sarajevo Winter and Los Angeles Summer Games.

Meantime, workers in factories throughout Yugoslavia have been setting aside a small percentage of their incomes to help cover the remaining costs of the Olympics.

To house the 12,000 athletes and officials and the 5,000 press expected, two complete settlements are being built in the vicinity. They will be handed over to municipal authorities afterward to help alleviate a chronic housing shortage in this city of 450,000.

Existing hotel facilities won't be enough to accommodate a projected 30,000 tourists for the Games, so the plan is to put many of them in the homes of willing area residents.

Getting visitors into Sarajevo by air could be another problem, given the city's famous fog. The airport is being equipped with a more advanced landing guidance system, but in addition, local organizers have ordered express trains and buses to transport people from alternative Yugoslav airports.

Once here, visitors are supposed to be spared the traffic snarls that marred the 1980 Lake Placid Games by a regimented one-way loop road system to mountain sites.

The pre-Olympic competitions in Sarajevo this winter produced relatively few complaints from international sports officials and athletes.

Among the criticisms, the men's downhill run was said to be too bumpy at the bottom, the ski jump landing area wasn't sloped quite enough, and the bobsled track had too much ice collected on a few turns. Local organizers said these details can be easily corrected.

The most nervous moment for Sarajevo officials came in January on the day the World Cup men's downhill was supposed to start. The weather turned unseasonably warm, and the snow was melting fast.

"That day and night were very difficult," recalled Anto Sucic, a former Sarajevo mayor and current president of the executive organizing committee for the Games. Sucic said he was terribly worried then that his city would suffer an international embarrassment if the event had to be canceled. Fortunately, the mercury dropped the next day and the ski competition was run.

In diverting precious Yugoslav manpower and materials to stage the Olympics, officials here know much is at stake. The gamble, they said, is not simply to pull off the Games. The real payoff will come only if Sarajevo can capitalize on the two weeks of worldwide coverage of the Olympics and sell the city as a new winter tourist attraction.

"I think of the Olympic rings as flying saucers," said Lukac, referring to the emblem of the Games, "because without them, we'd never be traveling so far."