Thomas J. Abinanti, a Democratic assemblyman from Westchester County, was driving to Albany on the Taconic State Parkway in January when his car struck a pothole. He made it to the capital, but the tire had to be replaced. A few weeks later, he hit another pothole, this one on Interstate 95. Limping off the exit ramp in Mamaroneck on the dented rim, he pulled into a nearby gas station.

“Here comes another one,” the attendant said.

At the other end of the state, Melissa Vacarro, a receptionist at a factory in Buffalo, was going home to Cheektowaga on Route 33 one day this past winter when her car plunged into a pothole, a hazard she said she had reported to the State Transportation Department twice. She lost both passenger side tires, and both wheel rims. The bill was nearly $4,000.

Winter always wreaks havoc on roads, but the onslaught this year transformed ribbons of asphalt into pockmarked lunar landscapes rarely seen.

Still, New York drivers looking to Albany for financial relief from winter’s wrath, like Mr. Abinanti and Ms. Vacarro, are bound to be frustrated by a mind-boggling legal anomaly: They are not entitled to file a claim against the state for damages.