A Washington father recently took his two children to see the New York City Ballet performance of "The Nutcracker" at Lincoln Center. At intermission he wouldn't let them leave their sets. After the performance he rushed them to a Fifth Avenue store to buy them each a new coat. "I've never been so humiliated," he said when he got back to his office. "I even put the coats on my own charge account."

It's true, there is a difference in the way kids dress for the ballet at Lincoln Center and the Kennedy Center, an old saw that has long held true for their older counterparts.

Kids have few occasions for really dressing up these days. When they are strictly among their peers, at birthday parties, the temptation is to dress casually - the girls in pants and tops, the boys in sweaters and coduroy jeans.

But when they're out with their parents as at Sunday Mass, bar mitzvahs, weddings, and particularly a grand occasion like "The Nutcracker," dressing up is trendy, even chic. And the difference in the style of dress between Washington and New York shows up as much in the kid's clothes as in their parents' outfits.

A a recent performance of "The Nutcracker" in New York, it was clear that kids, through their parents, had received the last word from Paris on hemlines and silhouttes. Easy fitting, chemise style dresses of mid-calf length (and coats long enough to cover them), lace collars and lace trims, boys in three-piece wool suits with conservative ties, no small number of them accompanied by mothers in the fur coats of the season.

Coats with matching hats, old Best & Co. style coats in plaid with velvet collars, fur muffs, tyrolean embroidered coats and an occasional fur coat round out some of the New York kids dress-up clothes for the ballet.

In Washington, the look is more cute and casual. For girls long dresses (to the floor) are perferred to the more stylish longer-than-knee length. Jumpers here are often worn with turtleneck pullovers whereas in New York they are frequently paired with lace-trimmed blouses.

It's cute and casual for boys, too. Turtleneck pullovers have remained more popular in Washington while in New York many of the youngsters at the Lincoln Center were in shirts and ties. and many boys in the Washington audience were wearing leisure suits, but no sign of them in New York.

"The Nutcracker" is still the biggest dress-up wearing more skirts and dresses for school, many stick to pants for birthday parties. Mira Suarez wears her best dresses for Sunday mass, but prefers pants for parties. Michele Ginsburg usually opts for gauchos when dressin for a birthday party.

When do the children stop dressing up for "The Nutcracker?" In both Washington and New York, the turning point for boys is 11 or 12. With the girls, there seems to be no entoff ages. Said Vera Silverman, at Lincoln Center, glancing at her sons Noah, 13, and Adam, 16, who were wearing jackets, sneakers and hiking boot, "That's what they call dressing up."