UPDATED 03/19/16 12:32 a.m.

NEW YORK (CBSNewYork/AP) — It has seemed like spring – and even summer – throughout much of the month of March, but winter may come back with a vengeance for the very occasion of the first day of actual spring.

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Forecasters say Sunday will start off cloudy and cold with a mix of rain and snow before changing to all snow Sunday night. Just how much snow will hit the area depends on the track of the storm, CBS2’s Lonnie Quinn reported.

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Late Thursday, three of four forecast models agreed that totals could hit the area hard, socking some parts of the area with 10 inches of snow.

If the snow system tracks tightly along the Eastern Seaboard, the totals will be higher, while if the system is centered over the ocean, conditions will be drier and snow totals lower.

Late Friday night, most of the models showed the storm tracking to the east — some so far to the east that they forecast the city getting no snow at all.

The North American Model, which successfully predicted the two-foot blizzard that socked the area in late January, was calling for no snow at all for the city and most of the area, and only 1.6 inches in Montauk. Most of the area would instead experience rain under the model.

The European Model, famous for its accurate and devastating prediction for Superstorm Sandy in 2012, showed the snowstorm bringing 3.2 inches of snow to the city, 3.3 inches to Coram, 2.4 inches to Brick, New Jersey, and 2.7 inches to Sparta, New Jersey.

The GFS model called for 1 inch for the city, and 2.6 inches for Coram, while the a fourth model, the RPM, called for no snow anywhere but 0.8 inch in Montauk.

Quinn said for his forecast late Friday, he now expects 3 inches or more just for Connecticut and eastern Long Island, 1 to 3 inches at most for the boroughs of New York City and most of Long Island, and an inch or less for the Jersey Shore and parts south.

But he warns that the totals could double or triple if the system wobbles just a hair to the west.

In advance of the likely snow, Mayor Bill de Blasio has ordered a travel advisory for the city for all day Sunday. The mayor warned that temperatures will only reach the 30s during the day on Sunday and will drop near freezing Sunday night.

The Mayor’s office advised driving slowly given possible icy conditions, using major streets or highways whenever possible, keeping a full gas tank, and avoiding slippery surfaces.

The forecast seems like something befitting of a remote arctic tundra compared with the conditions in New York City on Friday. The day started stunningly in Central Park, and people were out running, blowing bubbles, and even riding unicycles.

“Just too perfect, absolutely perfect – daffodils, forsythia, cherry trees blooming — what could be better?” said Joe Taylor of the Upper West Side.

And while some may like the idea of snow even this late in the year, Taylor most assuredly did not.

“Are you trying to give me bad news?” he said.

Some people simply didn’t believe the snow was even coming.

“I don’t believe it, not a word of it,” said Haig Casparian.

“I don’t believe it,” said Mona Fawzy of the Upper West Side.

But the weather forecasts agree that the snow will be happening, after what now seems like a big tease by Mother Nature.

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“It feels like winter’s been over for a while,” said Shauna Maty of SoHo.

Indeed, the last time we got snow was March 4, and that was less than half an inch. The rest of the month has been really warm, nearly 9 degrees above normal.

But be that as it may, the beautiful spring colors may well soon be mounted by falling snow.

“Not looking forward to snow on Sunday, but I love it today,” said Barbara D’Elia of the Upper West Side.

But D’Elia said she will go ahead with her brunch plans anyway.

“(We’ll) have some bloody Marys and enjoy ourselves” and warm up, she said.

“It’s appropriate,” added J.P. Partland. “We’ve had plenty of late March, early April snows in the past. It’s a reminder of what weather should be like.”

But if some models prevail, we actually may set a new snowfall record for the date of March 20. The record for Central Park for that date is 4.7 inches.

As for the latest snowfall of the season – meaning more than a trace on the ground – that happened on the date of April 19 with 0.8 inch.

This weekend’s snow will also fall on the city’s half marathon, but J.C. Zavala of Boston is just fine with that.

“I was hoping for sun like today, but I’ll take it,” he said.

He said he will add just a few extra layers to his attire for 13.1 miles.

“I’ll definitely have a winter hat, gloves — that’s it,” Zavala said, “so it should be perfect weather, actually.”

Mike Gansmoe has been getting ready for the Macy’s Flower Show, just in time for the weather to backpedal from flower season to road salt season. But Gansmoe, the executive producer of the show, was unflappable about it all.

“I say bring on the snow,” Gansmoe said. “We’re going to have spring here in Macy’s.”

He said setting up spring indoors takes a year’s worth of planning.

“It’s hundreds of people, thousands of hours over two weeks to install it here in the store,” Gansmoe said.

With more than 1,000 varieties, the vibrant displays should help warm people up as the temperature drops and the snow falls.

Meanwhile, Luna Park at Coney Island in Brooklyn had been set to hold its opening ceremonies on Sunday. The opening date has now been changed to Saturday, March 26, but the park will still be open Sunday – perhaps giving visitors the opportunity to ride the Cyclone roller coaster in the snow.

And for what it’s worth, the snow probably won’t stick around for long. The forecast is calling for temperatures to be in the 40s Monday and Tuesday before climbing above normal later in the week.

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(TM and © Copyright 2016 CBS Radio Inc. and its relevant subsidiaries. CBS RADIO and EYE Logo TM and Copyright 2016 CBS Broadcasting Inc. Used under license. All Rights Reserved. This material may not be published, broadcast, rewritten, or redistributed. The Associated Press contributed to this report.)