The PS All Season 4 should be able to hold their own in the snow. It's certainly not a winter tire though.
I see that it's marked as a T0 tire, which is awesome. This means that it's specifically tweaked by Tesla and Michelin for the Model Y. They probably added the interior foam to reduce noise and adjusted the compound for reduced rolling resistance.
Here's a helpful review comparing the generic PS AS4 to the PS 4S and X-Ice tires in the snow. The summary is at 13:52.
The Tesla specific T0 tires aren't available at Tirerack.com yet but here's their review of the generic tire's winter performance.
"we can confidently say Michelin's new UHPAS tire is a strong performer in light snow."