BELFAST — The wind was whipping fiercely at 3:30 p.m. in Heritage Park near this city’s waterfront, creating wind chills well below zero.

But two ice sculptors, swaddled in winter garb, worked steadily with their small chain saws to create an icy icon of New Year’s by the Bay, a festival of the arts lasting from 3 p.m. to midnight. “BELFAST ’98” read the car-length ice sculpture, topped off with a chubby four-car train of ice.

By all indications the two men seemed to be toiling in a city not interested in the inaugural New Year’s by the Bay. But by late afternoon families were steadily making their way into churches, studios and stores to watch or take part in dozens of events. Few, however, were tarrying on the streets.

By 5 p.m., stores had run out of $5 buttons needed for admission to each event, and organizers instead started to give coupons. Jennifer Hill, the New Year’s by the Bay coordinator, said it looked as if there might not be enough coupons. About 2,500 buttons had been made and passed out to stores throughout mid-Maine, Hill said, but organizers won’t know for a few days how many out-of-Belfast buttons were sold.

“This place was chaotic for a while,” said Mayor Page Worth at City Hall at about 5 p.m. “A lot of people were coming here looking for buttons,” she said. City Hall was supposed to have been the event’s headquarters more than a place to buy buttons, but the law of supply and demand seemed to have driven would-be revelers to what they perceived as the button source.

According to Worth, several motels had filled up for the night. Though it was early in the evening, Worth declared the event a success. “I love to see all the children out with their parents,” Worth said. “So often parents aren’t with their kids on New Year’s Eve.”

With wind chills at times unbearable, families moved briskly from place to place.

Gary Bosk of Belfast walked into the First Baptist Church on High Street with his wife and two children, Matthew and Lindsey. Just finished with a 15-minute horse-drawn carriage ride, Bosk vigorously wiped the frost and steam from his eyeglasses as he directed his children to the puppet making taking place in the church basement. Bosk had several events planned for his children this evening, including Hawk Henries, an American Indian flutist performing in the nearby First Church of Belfast, the Liberty Balalaika Ensemble and Celtic dancers.

“We’re kind of playing it by ear,” Bosk said, echoing the approach of others wandering about downtown Belfast. “At some point we’re going to bring the kids home — we’ve got a sitter lined up — and then we’ll come back. We want to see the fireworks.” That display was to signal the new year at midnight.

Some venues were crowded to capacity. Funnel, a three-piece acoustic band, played reggae-tinged songs at Krazy Kones, an ice cream shop on Main Street, to a full audience — an audience in which nary a cone consumer could be spotted. Watching performances, it seemed, was as much a chance to warm up as to enjoy the arts.

The flow of people was constant in and out of each performance. As the Penobscot Bay Scottish Country Dancers hopped around the First Church Parish Hall with willing and not-so-willing volunteers from the audience, the stairwell leading up to the hall remained busy with traffic. A group of five young boys rushed up the stairs and huddled by the open door leading to the dancing. The looks on their faces made it apparent that they probably had seen little Celtic dancing and probably fewer men wearing skirts.

As one boy regained his composure, he said to the others, “Let’s find the food.”