Summary: There’s no doubt that conditions are thin on the trails closest to NYC, but there is skiing to be had. Best bets are Mohonk and High Point:
“After checking in with the staff they felt that the Upper Awosting trail (Green) held the most snow. The rest of the trails that they attempted to groom had rocks showing through and bare spots”
Conditions at Minnewaska State Park (via mhvxcs Google group)
“We will roll the trails for classic skiing, and the roller will leave tracks. There is not enough snow for skate skiing. The trails with a thick layer of wood chip rquire little snow to ski, and the areas of the trail system with grass should also be acceptable.”
High Point trail conditions (via website)
“Fresh powder, thin coverage Outer trails ungroomed”
Mohonk Mountain House ski conditions (via website)
That said, much better skiing is easily findable for just another hour or so of driving. Canterbury Farm is reporting good skiing, as are Notchview and Prospect Mountain. Pineridge and Northfield is open again after a long hiatus.
Here’s a daytrip range snow depth graphic:

The difference between Mohonk and Minnewaska today are partly in the reporting interpretation, and some relating to trail surface (Mohonk dirt trail vs. Minnewaska carriage road gravel/dirt). Same for High Point.
Across the larger region there’s a pattern I saw last year, in that much better skiing is found at the touring centers that can hold onto a base; even a minimal base of ice is a much better starting point than bare ground.
The usual update has been made to ‘State of the touring centers‘, with the Word including the amount of new snow since yesterday. BETA has not reported since yesterday, but I’d assume backcountry skiing is much better. Here’s the regional snow depth graphic:

Despite a warming trend starting Thursday, areas like Notchview, Prospect Mountain, and Brattleboro will probably be able to hang onto skiable trail through the end of the week.
Happy skiing!