YOU KNOW what Teddy would like?" asked Gretchen Mobberley as she sat on her huge chestnut gelding talking to a group of children, some of whom were having second thoughts about being so close to such an enormous animal.

"Teddy would like a carrot," Mobberly went on. "Do you you have an extra for him?" Behind her, riders and officials were slowly assembling for another point-to-point race across the Howard County countryside.

A young girl shyly pointed a carrot through the snowfence and Teddy Bear stretched his long nose and nibbled. "Teddy won't hurt you. He's a very, very sweet guy and he's very gentle," Mobberley reassured the youngster.

This sort of informal get-together between small children and big horses happens all the time at area Saturday afternoon steeplechase meetings. Patrol judges and outriders, like Mobberly, often gather near the finish line between races to chat and show off their horses.

A growing number of Washington families are discovering that point-to-point racing is a springtime family delight.

"People think of horses in terms of racetracks and betting," says John Durham, a Silver Spring father of three who likes the races because they provide "a lot of fresh air and give you the chance to see varying types of people that you wouldn't normally see. It's not like a racetrack where you're crammed in and kids get bored. Steeplechasing is a unique resource of this area."

It's also generally cheaper than a ballgame in Baltimore, and a lot less nerve-wracking than a trip to a theme park.

The sport was born in Ireland almost 200 years ago when gentlemen raced from village to village, with church steeples marking start and finish.

Washington is the center of American steeplechasing. There are eight courses within a 90-minute drive. Between races the rolling countryside and open pastures invite lacrosse or touch football games.

"My daughter really loves the animals," said Margaret Rose Durham. "You can get up really close to them and watch. I'm a little afraid of them, really. But it seems to be very popular with girls."

Watching the other spectators is fun too. Steeplechases attract as varied a bunch of spectators as you're ever likely to see. They range from Virginia's tweedy "kissin' cousins" to Potomac's easy-come, easy-go BMW set; from telephone operators to Southern Maryland trash haulers. Lately, young people wearing spiked heels and spiked hair have added new contrast.

Horse racing may be a rich man's game, but the spectating is cheap. General admission ranges from $3 per person to $5 to $20 per car. Children 12 and younger are almost always free. Prime parking spots along the finish line are usually available several weeks before race day at additional cost.

And you needn't spend days in the kitchen frying chicken and baking deluxe pastries. Many a fast-food bag has been spotted crumpled among the silver candlesticks and flower arrangements along the tailgates.

"This is one of the best things about living in Maryland," said Nancy Hammond of Annapolis, as she stood with friends on the hill overlooking the Marlborough races recently and watched her 13-year-old son Richard toss the football with friends.

'Chase meetings in Virginia offer six to ten races on a day's card. Marylanders usually hold the card to two or three races. But fewer races don't seem to keep the crowds away. Each year as many as 15,000 fans are attracted to Glyndon, in Baltimore's Worthington Valley for one race, the four-mile Maryland Hunt Cup, considered to be America's toughest steeplechase.

Steeplechases have become as much a social outing as a sport. "We have friends who just moved here from California and they don't have things like this there. It's great to take friends from out of town to see the races," explains Durham. "And kids love them." HINTS FOR HUNTS

Although steeplechase courses may be only 65 miles away from town, the air's usually cooler in the mountains; dress warmly. Spring means rain. Boots or rubbers and a raincoat will often save the day. Leave pets at home. THEY'RE OFF!

There are several more weeks of steeplechase racing before summer:

SATURDAY Fairfax Hunt features pony race at noon and six-race card beginning at 1 at Belmont Plantation on Route 7 near Leesburg. General admission, $5 per person; children under 13 free. Call 703/777-3805.

SATURDAY -- $12,500 BMW Grand National timber steeplechase plus two other races, in Butler, Md. Post time is 3:15. $10 per car. Call 301/667-9000.

SUNDAY -- Middleburg Spring Races. Carriage parade at noon, post time for first of seven races is 1 o'clock at Glenwood Park. General admission, $5 per person; children under 13 free. Call 703/687-6545 or 6595.

APRIL 27 -- Foxfield at Charlottesville. Six races beginning at 2. $5 per person. Call 804/293-9501.

APRIL 27 -- 89th Maryland Hunt Cup, Glyndon. One race at 4. $20 per car. Parking stickers must be purchased in advance. Call 301/667-9000.

APRIL 28 -- 34th Potomac Point-to-Point Races at Belvedere Farm. Nine races beginning at 1. $10 per car. Call 301/338-7500, 862-2873 or 840-2254.

MAY 4 -- 60th Virginia Gold Cup at Great Meadow, The Plains. Seven races beginning at 1:30. $7 per car in advance, $10 race day. Call 703/253-5001 or 703/347- 2612.

MAY 27 & JUNE 8 -- Fair Hill Races, Fair Hill, Md. America's only full card of steeplechase racing offering legalized parimutuel wagering. Eight races each date beginning at 1:30. Bleacher seating available. Call 301/398-6565.