An approaching cool front will bring the coldest weather of autumn so far as we work into Tuesday, Wednesday, and Thursday. The front will bring mostly light precipitation as it drops south through the region early on Tuesday morning but it will bring showers that may transition from rain to snow by the time the front clears the region early Tuesday.
So, yes, it *may* snow early next week. Just not in heaping quantities that some had hyped up.
The front that drops south early Tuesday means a bit of business by mid November standards -- highs will not reach 50 for at least two days, perhaps three. I won't call it arctic air (some will, I won't) but the air that's pushing south will be chilled enough that lows will drop into the teens in the Pennsylvania mountains on Tuesday night and Wednesday night.
It's going to also drop a good ways south as well as it pushes down -- bringing the season's first frosts and freezes down into the Deep South by Wednesday morning. It's November and it's not unusual for this to occur. Last November had 11 days that failed to reach 50 degrees. The average November has about eight such days. That said, the push of chill will be the strongest to date and probably brings Philly an honest-to-goodness freeze on Tuesday night (20's possible even at the Airport).
The strong high responsible for this push of chill is also strong enough to suppress the track of a disturbance that pushes down along the front into the South. This disturbance will develop into a storm in the Atlantic but, as of this morning, modeling is in agreement that the storm does NOT impact Philadelphia. The Euro does develop it closer to the Carolina coastline but keeps precipitation far enough to our south where we're dry. This *could* change if the disturbance gets in a bit quicker, the high comes in a bit slower, the disturbance is a bit stronger diving down out along the front. Those things look less likely for a scenario that didn't look terribly likely from the get go given the immense amount of waffling within the modeling, as well as between modeling.
That said, the frontal push on Tuesday morning could bring the season's first snowflakes to you...but they will likely be flakes only.