At least 55 people have died in US weather-related incidents since late last week, according to NBC News
It comes as road and utility crews struggled to dig out the snowed-in region around Buffalo.
Erie County executive Mark Poloncarz told reporters on Monday that the county's tally of storm-related deaths had jumped by 12 overnight, and included cases of people who were found in snow banks, in their cars or who had died from cardiac events while ploughing or blowing snow.
More deaths had been reported, Mr Poloncarz said, but the county medical examiner was trying to determine if they were directly attributable to the weather.
"There still are probably additional deaths that will be announced later today," he said.
At least 55 people have died in US weather-related incidents since late last week, according to NBC News.
The storm wreaked havoc with travel across the US over the weekend, stranding passengers as thousands of flights were cancelled.
The blizzard, deemed the Buffalo area's worst in 45 years, struck late on Friday and pummelled western New York through the Christmas weekend.
It capped an Arctic freeze and winter storm front that had extended over most of the US for days, stretching as far south as the Mexican border.
The greater Buffalo region, on the edge of Lake Erie near the Canadian border, has been one of the hardest-hit places, with nearly 50 inches of snow recorded at Buffalo Airport on Monday morning, according to the National Weather Service.
Cars and buses were buried under towering snow drifts and high-lift equipment was being used for hospital transports where ambulances could not drive.
A few grocery stores that had been closed for days reopened on Monday, and people trekked more than a mile through the middle of the impassable streets to get there.
Up to a foot of snow was still forecast to fall on Tuesday in some areas south of Buffalo and north of Syracuse.
Heavy winds and "lake-effect" snow - the result of moisture picked up by frigid air moving over warmer lake waters - produced a storm that New York Governor Kathy Hochul said would go down in history as "the Blizzard of '22", ranked as the worst since a 1977 blizzard killed nearly 30 people.
President Joe Biden tweeted on Monday that he had spoken to Ms Hochul on the phone and that his administration would provide resources to help the region cover the daunting expense of storm rescue and recovery.
"My heart is with those who lost loved ones this holiday weekend. You are in my and Jill's prayers," Mr Biden said.
Hundreds of national guard troops were assisting local first responders and state police on Monday as crews rescued people trapped in homes and cars, performed wellness checks and delivered food and basic needs.
Emergency workers have struggled to navigate past snow drifts to do their jobs. Many snow ploughs, tow trucks, ambulances and other emergency vehicles dispatched over the weekend had to be rescued themselves after getting stuck in the snow.
Thousands of people in Erie County had power restored on Monday morning, while some 14,000 customers were still without power statewide.
A driving ban was still in effect in Buffalo on Monday, for safety purposes and to keep the roads clear for emergency and utility workers trying to weave through an obstacle course of buried cars and snow banks.
"There are cars everywhere. Everywhere. Pointing the wrong direction on roads. They've basically been ploughed in and they need to be dug out and towed. It's going to take time to clear those," Mr Poloncarz said.