The first low in modern history to originate from the Gulf, pelt DC and bury west of them and then head ENE. 999,999 out of 1,000,000 times we'd be heading for a SWFE.
The event next week looks like a Hunchie deal on N and NE for a few inches. The other one a few days later may have some legs, but being the 26th means normal caveats apply. After that, looks like we turn milder.
I don't think the sleet that far north means much. The forcing and air flow will shunt that ENE anyways. Basically it means a more narrow all snow area near NJ and NYC.