Rocca and his wife, Christine, have driven pairs—two horses pulling a carriage—for years, but their new quartet was not quite ready to perform last season. “In public the horses are really put to the test as to whether they can behave,” Rocca says.

For the drivers, called whips, and their passengers, a select but growing number of carriage events in North America and Europe beckon. Driving clubs sponsor some of the races, while some are private parties reserved for the inner circle. Weymouth, who discovered this pastime more than 40 years ago, has witnessed it make great strides. When he joined the local Four-in-Hand Club in the early 1960s, it had five members; now it has 52. Weymouth’s passion kindled when he moved to his mid-18th-century house—Big Bend—in Chadds Ford, Pa., and decided he did not want cars to taint a landscape that had changed little in two centuries. “People had old carriages in their barns and began to see using them as a lost art,” he remembers. In 1995 Weymouth painted a commissioned portrait of Prince Philip, also a driving aficionado whose image has helped popularize the sport.

On both sides of the Atlantic, exclusive clubs of horsey types gather for days at a time, in events that are more social than riding: A carriage ride is basically a rolling party, the driver, however, must have a special gift for communing with horses, while the team of steeds must match like bookends in looks and temperament. Most of the events are organized by invitation only. To be a member of a driving club, you have to be a master whip, which entails investing not only in the carriage, the horses, driving lessons and continuing clinics, stable personnel and accoutrements, but also in a way of life. Donald Rosato, a former Philadelphia physician, employs grooms who wear livery and sound the hunting horn when he takes off in his Holland & Holland roof-seat brake carriage. Rocca exercises his horses four or five mornings a week. “They have to be conditioned, just as athletes do,” he notes.

The public sees the events that involve parading on racetracks, across polo fields or through town squares. For race-day parades, carriage drivers and passengers dress to the nines, men in top hats and women in the kind of millinery Judy Garland wore in Easter Parade, downing champagne and waving to beer-drinking throngs of tailgaters wearing flip-flops. Weymouth requires that his guests look contemporary but elegant when they parade on the steeplechase track. “To keep the sport going, we try to keep up the traditions of driving,” he says.

On long country drives, riders wear sportier hats and let their hair down a bit more as the day wears on and Bloody Marys flow. These private drives are commonly held on estates. Last year, during the Strawberry Hill event, Harrison Tyler, a descendant of President John Tyler, hopped aboard the carriage of Rolf and Carol Van Schaik of Cavendish, Vt. They led the procession through the Fort Pocahontas Plantation, a Tyler family estate along the James River in Virginia. The day ended as driving days always do, hosing down sweaty horses and scrubbing every single piece of harness, with minutes to spare before the evening party began.