It may be the Year of the Horse, but it was the Day of the Shoulder - the paternal Shoulder - for countless children who came to see yesterdays Chinese New Year celebration.

"I see a dragon," said the top half of one father-son act.

"I see two dragons," said an adjacent youth, likewise riding a pair of shoulders.

"I see a dragon with two heads," came the first youth's rejoinder.

At this, the head attached to the shoulders below spoke up for the first time. "You must have had something the drink like I did," it said.

A child standing on mere pavement was pleading with his mother to describe the dragon or dragons beyond. "I have no idea if there's a dragon or not" said his mother. Turning to a friend, she added, "I just love all these short little fathers getting these reports."

For some offspring, the supreme vantage point carried with it a certain element of risk. "Don't let go!" screamed one child to his father underneath. "I won't let go," the father replied indignantly. But his son was unmollified. "I want to get down, you stupid man!" he declared.

So down he came, his father making a feeble effort to conceal the hurt. Luckily, a willing sibling was available."Come on up," said the father to the sibling, hoisting her into the air. About two feet off the ground, there was sudden and unexpected resistance. "Don't you get me on your darn old shoulders!" instructed the sibling.

"What if that dragon eats me?" inquired still another daughter of still another father.

"You don't have anything to worry about," replied the father, "because he only eats little girls whose names begin with 'R' who are 5 years old."

A block further up H Street, Harrison Lee of the Chinese Consolidated Benevolent Association was overseeing the dismemberment of his 26-man, 200-foot-long bicentennial dragon, which has been living in Lee's home since 1976. "I put this thing together," said Lee. "It came as a do-it-yourself kit."

For avowed and prospective mayoral candidates, yesterday was a stern test. Although the temperature was in the '40s, once the sun had receded behind the On Leong Chinese Merchants Association, there were widespread mutterings about the cold.

City Councilman Marion Barry, Council Chairman Sterling Tucker and Mayor Walter E. Washington all wore heavy topcoats and serious expressions as they waited through announcements of lost and found children, the United States and Nationalist Chinese anthems as played by the McKinley High School band, and several speeches delivered in English and Chinese. When Barry applauded, he did so without removing either hand from its chosen coat pocket.

A few hundred feet west, and about 30 degrees warmer, Police Chief Burtell M. Jeferson and former Chief Maurice Cullinane enjoyed a panoramic view of the day's proceedings from their window-front table at the China Inn Restaurant, while ploughing through an eigh-course dinner in honor of the new year, 4676.