At this point nobody in a position of authority (Caltrans or the Park Service) seems to have spoken to this. I assume we might hear something in the next few days; I would suggest using a news search engine to look for recent articles containing "Tioga".
My personal guess is: No, this is not the final closure. It looks to be a one-off early season storm, and a warm one at that. I think they'll probably get CA120 open again, but I have no idea when that might be.
The Tioga webcam referenced earlier on this thread is a blur this morning.
Here's where you can get realtime highway info; plug in 120 to see status of Tioga Pass (currently closed).