By afternoon, snow had turned to sleet in areas of southeastern Massachusetts, as well as parts of Cape Cod and the islands of Martha's Vineyard and Nantucket.
Dunham said the worst of the snow was just about over by 1 p.m.
A winter storm warning was maintained until 1 a.m. for northern parts of the state because a little snow was expected to linger.
No significant power outages were reported.
Some people had no choice but to drive on the slippery roads.
Ann Scagel, of Haverhill, about 35 miles north of Boston, said she had to drive her daughter to her job at a supermarket.
"People shouldn't be on the roads if they don't have to," Scagel said. "I am going to try to get out of this mess and home as quickly as I can."
Dan Volonino, 72, of Haverhill, did not let the storm stop him from sticking to his New Year's resolution to work out. He was at the gym at 9 a.m.
"I think God is punishing me for all the mean phone calls I had with my children when I was spending my winters in Florida," he said. "I used to call them and complain about having my AC on while they were stuck in snowstorms."
Larry Hardin, of Arlington, said he has a simple philosophy for keeping up with the shoveling.
"One shovel at a time," he said.
Associated Press writers Rodrique Ngowi in Arlington and Paige Sutherland in Haverhill contributed to this report.