A 2 Tuesday morning, on a farm nine miles outside Elmore, Minn., 18-year-old Beth Hinrichson got up to come to the parade. It was 20 degrees below zero outside, with blustery winds over the frozen fields, and in the quiet of her room, Miss Hinrichson took down her unfirom: the blue velvet dress, the white boots, the baton she would use to lead the Elmore High School Band up Pennsylvania Avenue on inauguration day.

If I make a mistake, Miss Hinrichson thought, the whole band is going to mess up.

All this week the buses have rumbled toward Washington. They pulled out of parking lots in Oil City, Pa., in Colby, Kan., in Princeton, Ind., and Platte, S.D. They carried the Fighting Tigers of Wilmington, Del.; the Marching COlonels of Henderson, Ky.; the Marching Indians of Toms River, N.J. They carried tubas and snare drums, bagpipes and glockenspiels, with enough velvet and glitter to light up the city for Jimmy Carter's first presidential parade.

Airplanes lifted away from Denver, from Honolulu, from San Francisco. From Colorado and Long Island and Illinois came horse trailers crowded with Morganas, Arabians, Clydesdales, Appaloosas and mules. In Anchorage, a 71-year-old former dogmusher to Adm. Byrd led this dog team into a truck, tied his sled to the roof and headed south for Washington.

The cavalry arrived yesterday morning Equipped with brass sabers, black-powder pistols and carbines, and blue hats emblazoned with crossed swords, the Springfield 7th Illinois Cavalry, Reactivated, rattled into Rosecroft Raceway at about 9 a.m. in a long caravan of trucks and horse trailers. Gingerly, eyeing the ice that glazed much of the ground around the stables, the riders led their mounts to the stalls.

The cavalry was reactivated last year for the Bicentennial and rides now with much of the original Cavil War tack. "We kill Johnny Rebs," explained Dr. Karl Luthin, Company C captain, in a startling display of Northern chauvinism.

The Biddeford Tigers Marching Band pulled in at noon, four busloads of musicians and majorettes and bleary-eyed chaperones.They unloaded at the Southgate Motor Hotel in Arlington, 14 hours and one bus breakdown after leaving Biddeford, Maine, where the winter has been so fierce, they said, that school closed down for six days.

They were tired, the Tigers said, but not nervous. Too feisty to be nervous, they said. "We are never scared," scoffed Celeste Houde, 15, who plays the flute.

In Baltimore, the 135 members of the Alexis I. du Pont High School Band - also Tigers, but Fighting Tigers - scattered in the Holiday Inn late yesterday afternoon. They had left Wilmington, Del., in the early afternoon, after a frantic last-minute search for enough white tubas to color coordinate the band.

"This is our first time on national TV," said Mandy Kephardt, a school senior who is both librarian and clarinetist for the band.

Miss Kephardt allowed as how she was a trifle neruous what with keeping seven people in a line, playing the music properly, and fingering a clarinet in icy temeratures with no gloves.

Severe cold, in fact, is a marching band's greatest enemy. When the temperatures drop much below zero, several uneasy musicians explained yesterday, the valves on the brasses freeze. They can freeze either raised or pressed down, giving rise to the some band will round a corner and alarming possibility that, for example, find its trumpets stuck in E flat.

That is only one of the small traumas that can befall a parade, and the preinaugural preparations have been filled with uncertainties. Will the anti-freeze in the California float keep its waterfall gurgling smoothly over its wood-and-chicken wire mountain? Will April Boy, the Morgan horse ridden lovingly for the last five years by 16-year-old Kelly Henry, of Rochester, Ill., lose his footing on the ice?

Will Bob Cook, the Air Force driver pulling the huge U.S.A. float, negotiate the troublesome corner of 15th and Pennsylvania Avenue? Will the Dundee Scots, from Carpentersville, Ill., find their bagpipes silenced by the cold?

There are contingents of parade coordinators, both military and civilian, trying to prevent as much mishap as they can. The 75th Engineer Battalion, out of Ft. Meade, Md., spent the day yesterday chipping away at the ice along the parade route, and military officials are working out of a thick instructional booklet that includes chapters on Parade Division and Control Instructions, Communications, and Logistics.

It is all very precise. At 13:34 hours (1:34 p.m., civilian time), the first unit of the first division, a motor-scooter escort from the D.C. Special Operations Division, is to roll past the intersection of 3d Street and Pennsylvania Avenue. Behind it the contingents will move out 10 yards apart at 100 yards per minute - 120 steps per minute, for feet, and about 3 m.p.h. for floats.

The floats, as usual, will be brilliant, rolling islands of local pride: a Samoan hut, a Tennesse barn dance, a 12-foot missile, solar-heated house, a giant helium-filled peanut, a steam-engine locomotive (with two cars), and Charles Lindbergh's first airplane, will all roll past the new President this afternoon.

There are no flowers on these floats - real flowers can't take the cold, explained a representative of the hargrove Co., a Prince George's County firm building many of floats. But the float builders all make liberal use of vinyl floral paper, a shaggy, fabric-like paper, stapled right onto the plywood float base.

No. 197, a huge, damp warehouse latticed with high rafters, flat farm wagons slowly sprouted shrubbery, trees and giant suns as more floats took shape. A fat, styrofoam walrus, with white whiskers and a slightly pompous smirk, was being positioned on the front of Alaska's float Tuesday morning. Sheldon Fish, the walrus's creator, looked on with approval.

Fish is art director for the Phil Turner Display Company in New Jersey. The Alaska float, he explained, was designed by the company after consultation with Alaskan officials, who had asked for a theme of naturalism and ecology. Father down the warehouse, builders from an Alexandgiant U.S.A. float that is supposed to set the people's inaugural theme for the parade.

The paneling, which covers the top and sides of the rolling letters, is all mirrors. "Everybody'll be seeing it," a workman said, standing back to admire the float, "and they'll be looking at themselves as it's going by."