A few hours later, state troopers picked them up and brought them to a nearby police station, where another bus was waiting to take them back to campus, Niagara guard Tiffany Corselli said.
Niagara coach Kendra Faustin said everyone was OK and the team was in good spirits. Players had been running low on food, but local officials dropped off snacks and drinks. There were 25 players and coaches aboard the bus as well as Faustin's 1-year-old son.
"We have snacks, some granola bars and pretzels," Faustin told The Associated Press in a phone interview prior to being picked up. "We found six bottles of water and have been rationing it. We thought we'd be here for a couple hours and a couple of hours turned into 12 hours. It's now 24 hours."
Before the supplies arrived, the team actually turned some of the snow into water. Faustin described snow drifts higher than 6 feet that covered cars. Other motorists had come aboard the team's bus seeking shelter and bonded with the team.
"It started to get bad fast at about 2 a.m. [Tuesday], and we came to a dead stop and haven't moved since," Faustin said. "It was a rough weekend for us on the court and it just won't end."
The coach told the AP during the ordeal that the team had heard on the radio that all stranded motorists had been rescued, but "apparently they missed us."
In a region accustomed to highway-choking snowstorms, this one has been called one of the worst in memory. Snow blown by strong winds forced the closing of a 132-mile stretch of the Thruway, the main highway that runs across New York State.
Faustin had told ESPN during the ordeal that the bus had enough gas and power to last a few more days.
Meanwhile, the team had taken to social media to tell others of their plight and post selfies.
"This whole Twitter and media thing has kept their spirits high," Faustin said. "It's something fun for them to do."
The team also watched movies and caught the Duke-Michigan State men's basketball game on ESPN on Tuesday night.
"They really have been great; there's been no complaining at all. They've been joking around: 'I want a steak, I want a soft taco, a Slurpee,'" Faustin said while they were stuck. "There's definitely nothing in the coaching handbook to prepare you for this.
"I'm sure when it's all done we'll look back at it and remember how great a bonding experience it was. For now I think everyone just wants to get home and sleep in their own beds."
The Associated Press contributed to this report.