MOSCOW, DEC. 8 -- The cold night and the remnants of a wet snowfall did little to dampen Muscovites' enthusiasm for watching the White House summit ceremonies beamed live tonight to television sets around the city and onto a giant screen that hangs high over the central Kalinin Prospekt.

It was 6 p.m. here when television showed the welcoming of Mikhail Gorbachev on the South Lawn of the White House, an event that became the focal point of many commuters' schedules. They then rushed home to watch the signing of the treaty on medium- and shorter-range missiles, which began here shortly before 10, halfway through the main news program.

Several hundred people sloshing their way home along Kalinin's sidewalks stopped in front of the giant screen to hear the two national anthems and the speeches by President Reagan and Gorbachev.

"It really is a historic moment," said Kolya, in his 20s, while his companion Natasha echoed the widely held view that Gorbachev's visit was just the first step on the road to a major warming of relations.

The excitement of the first visit by a Soviet leader to the United States in 14 years was infectious: on one corner of the sidewalk, people were taking turns talking by phone to Texas, while others were being interviewed for a direct broadcast by ABC television.

Several people with different political views said they were proud and pleased to see Gorbachev -- whom they called nash, "ours" in Russian -- carry himself so well in the White House, the quintessential American setting. Moscow television's commentary was minimal and neutral, while the official news agency Tass called the events "a remarkable milestone."

A TV commentator did say, "The majority of Americans are hoping for the success of the talks." The main evening news program was preceded tonight by a "telebridge" between teen-agers in Leningrad and Seattle, promoting similarities between young people in the two countries.

The day's upbeat tone was marred by the brief detentions by police of 14 Jews who were on their way to a demonstration protesting Soviet emigration polices. Organizers of the protest, the third scheduled in three days, said 16 other would-be participants were turned away as they made their way to Smolensk Square in front of the Foreign Ministry.

Four Soviet human rights activists reportedly were arrested as they headed for Moscow from the Ukraine to attend a human rights seminar due to start Thursday, according to Lev Timofeyev of the group called Glasnost. He said the four had been held on drug charges, which he has said in the past often are fabricated against activists.

The day's events began with an early morning taped broadcast ofGorbachev's arrival at Andrews Air Force Base, which occurred too late last night for live coverage here.

The next big event was the welcoming ceremony on the South Lawn, announced in advance on the day's television programs.

Some English-speaking Russians held their breath when Reagan in his opening remarks referred to the United States and the Soviet Union as "adversaries."

But in Russian, the word was translated as "competitors," so they breathed a sigh of relief.

Later in the evening, Moscow's Gorbachev watchers were equally relieved to see the leader in stride at the White House, as he traded jokes with Reagan while the two took turns at the White House microphone and went through the signing ceremony.

Yesterday, during the refueling stopover at Brize Norton air base in England, Gorbachev seemed slightly nervous as he spoke to the crowd at the airport, fidgeting with his fingers.

Several observers here had also found him nervous in the opening part of the NBC interview last week, when he hesitated over words and, in one case, misplaced the stress.

Soviet women viewing Raisa Gorbachev's wardrobe were quick to note that she has worn two different fur coats on the trip so far -- each of them different from coats worn last year in Reykjavik and at this year's Nov. 7 Red Square parade.

Raisa Gorbachev has many critics here who find her forward style unseemly.

Late tonight, Tass reported on the Soviet first lady's reception in Washington, noting that her arrival had evoked "tremendous interest" among Americans.

It noted that "lucky" journalists had posted themselves outside the Jefferson Memorial, one of her stops today.

"In my country, Jefferson is known as one of the world's greatest thinkers," Tass quoted her as saying. "It is very good that there is a memorial in his honor in the U.S. capital."