Nam mostly sucks. I would wait until tomorrow 12z runs to really see if that plume of moisture makes it north. That high is really pressing it so there’ll be some crazy precip gradients. Like philly could get 8 inches and we can get an inch. The precip is getting shredded by that stubborn high.
Give it a bit of time once the precipitation really develops the dynamic cooling will cool the columns and change the sleet up north to snow maybe even in New York City.
That warm air advection moves in after most of the qpf is done with. I still think nyc proper changes to sleet not rain, and after it gets a solid 1-3 inches. Bronx obviously has a higher chance at 3.