Thousands of happy people bundled themselves against the chill of the first day of December yesterday, then jammed into the trains on Metro's new Orange Line extension or strolled along the streets above to celebrate the subway's arrival in central Arlington County.

It was a day for smiling faces and hope-filled speeches, for ceremonies that included the American Legion and the U.S. Army Band, for wide-eyed children and impressed senior citizens who wandered down, as one said, "just to see what this Metro thing is all about."

It was also a day that served to underline Metro's political and financial difficulties. For while Virginia Gov. John N. Dalton came to pledge his support for the financially troubled Metro, he declined again to be specific about whether Metro could expect increased state aid or even whether Northern Virginia would be permitted to tax itself to pay Metro's bills.

The four new stations and three new miles of subway track bring to 33.7 the number of miles Metro now has in operation on its long-planned 101-mile system. That system is now projected to cost more than $7 billion. With the opening of the Ballston Line, costs have now reached $2.3 billion -- just short of the amount that was supposed to build the entire system when estimates were first made in the late 1960s.

One of the things Metro was supposed to do was bring life back to Arlington County's long-depressed Wilson Boulevard-Fairfax Drive corridor, and it certainly did that yesterday.

People were able to ride free between the four new stations until late in the afternoon, and they happily poured onto trains, rode to the next station, then looked around the neighborhood before pressing on up the line.

The color of orange was everywhere. There were orange streamers and orange balloons. The free passes, on orange stock, were handed out by Arlington volunteers wearing orange ribbons that read, "Follow our tracks."

Nancy Ness, the Florida Citrus Queen, smiled sweetly and clapped enthusiastically at appropriate moments throughout the day, and the Lions Club sold oranges (and grapefruits) at a stand outside the Virginia Square station.

Metro will start charging for rides on the Ballston extension today. If the system can solve its continuing financial problem, Ballston will be only a temporary end of the line until the middle of 1985, when Metro is scheduled to be extended from Ballston to Vienna, at Nutley Road and Interstate 66 west of the Capital Beltway in Farifax County.

Metro's planners predict that the Ballston extension alone will add 10,000 riders a day to the subway, which is averaging more than 260,000 a day now.

Metro is also bringing with it developmental pressures, as it has already done in downtown Washington, in Rosslyn and in New Carrollton, and those pressures are just as controversial in Arlington as they are elsewhere.

About 50 members of a group calling itself the Key Coalition picketed near the new Courthouse station early yesterday and caried placards that read, "Aren't Windfall Profits Enough?" and "Save our School." Their target was the Mobile Corp., which has proposed a complex of 12-and 16-story buildings across from Key Elementary School, near the station. The Arlington County Board is scheduled to act next Saturday on Mobil's request for the necessary rezoning.

The other visible protest yesterday came from a group of Arlington County employes who passed out pamphlets at the new stations complaining that Metro costs were draining local revenues and that county employes were paying for the drain through lower salaries.

The pamphlet urged Dalton to "pass a dedicated tax for Metro to relieve local tax sources" and pointed out that Metro pays third-year bus drivers $19,552 annually, while Arlington County pays third-year firefighters $15,310 and third-year teachers $13,011.

The day of Metro celebration began with a five-mile race run along the route of the new line. Jim Berka, a Department of Transportation civil engineer who lives in Ballston, defeated about 400 other competitors. He finished what he called an easy course in 25 minutes 7 seconds.

Meanwhile, underground, Jerry and Laurie Feinberg were riding the train. "We're Metro freaks," Jerry said. "We bought a home here [near the Clarendon station] specifically so we would be near the subway."

Edna Starkey, who lives a block from the Virginia Square station, was another early joyrider. "We waited a long time for this day and had to put up with a lot of construction and mess," said the waitress in a restaurant in the Virginia Square shopping center. "I think Metro is going to help a lot of businesses."

But Michael Tomic, owner of the Tennis Factory in Clarendon, was less enthusiastic. Timic recently received a notice that his $1.000-a-month rent would triple when his lease expires next year.

My landlady said it's a whole new ballgame for Clarendon with Metro," he said as customers milled around his pro shop. "So far business has been marginal, and we've been able to survive, but with an increase like that I guess I'll have to close."

American customers, rarely seen in the Indochinese shops along Wilson Boulevard, crowded the stores yesterday.

"Oh yes, business is better than usual," said Nguyen Hy, owner of the Pacific Oriental Department Store. "We think Metro is a good thing."

There were formal ceremonies at each of the four new stations, but the big one came in Clarendon in the early afternoon. Politicians and officials from across the metropolitan area gathered there to congratulate each other and to pledge completion of the system. About 1,500 people wedged into the intersection of Wilson Boulevard and Highland Street to applaud.

Gov. Dalton, in his speech, said it is essential that Congress pass a pending Metro financing bill and include extraordinary assistance to help defray Metro's mounting operating costs. Asked later if that meant he would oppose special state legislation for Metro if Congress rejects extraordinary aid, Dalton declined to answer the question directly. "I consider operating aid an integral part of the legislation," the governor said. He added he has "an open mind on the subject of Metro financing.

Area politicans are seeking help from both the Virginia and Maryland legislatures that would guarantee federally required "stable and reliable" operating funds for Metro.

Ultimately, the day belonged to the oeople, not to the politicians. James Jacobe, a senior at O'Connell High Shcool, took his first Metro ride yesterday before he volunteered to hand out maps at Virginia Square. "It's an experience," he said. "You could say that."