Snow: how deep is too deep for camping?

I'm sitting here in suburban Southern California, going stir crazy and looking at the snow depth monitors throughout the Sierras. They are slowly dropping -- yesterday we had a foot or more of snow in the higher elevations. Most of my favorite places still have several feet of wet snow. It will be mid-June before the snow is completely gone from the forest roads -- and there will be snow on the mountainsides all summer. How long do I have to wait?

So here is my question -- assuming that the forest roads are technically open, how deep is too deep? I have driven on and camped in six inches of snow. But the clearance under the axles of my truck and my trailer is about ten inches, I think. I'm guessing that ten inches is my practical limit. And there will be the occasional drift. I am willing to do some shovel work, but not an infinite amount of it.

I am sure someone with a monster truck and a truck camper could bulldoze their way into a foot or more of snow, but this is just a Tacoma -- more like a burro than a bull. ;)

Your thoughts are always welcomed -- at least it will help pass the time while we watch the snow melt.