Akichow, it'll be a while. They're simply trying to get Tioga clear right now, and using dynamite on ice around Olmsted Point.
Also realize that there are many use trails above the plateau section, which, if you're not used to seeing that sort of thing, can be confusing. Once you start heading for the summit, it's more of a "pick your poison" and steps to get there. It's not difficult route finding, by any stretch, but if you're looking for a solid, uninterrupted "trail" it will be different.
I'll put my money on late July/early August for full clearance. But it might stop snowing tomorrow...