If a total white out does happen, it doesn't last that long... except when it does last a long time. If it does, there is a number of massive boulders in which you could hide from the wind... except in the areas where there are no boulders. The Alpine Garden Trail comes to mind.
Anecdote: On the first time I climbed Mount Washington, I got an early start, got to the summit, shot a photo, and started down immediately. I reached timberline as the storm was hitting, so I reached the bottom safely and drove home. There was a stranger who had started from the bottom about an hour later than I had, so he got up near the summit and got pinned down out in the open when the storm hit. He was lucky enough to call 911 and reach the emergency dispatcher, so a rescue was called despite the terrible conditions. The rescue snow cat came up the road and found the stranger still pinned down, so they scooped him up and got him to the hospital.
Now, I'm guessing here, but if the storm hit before his call, and then the storm was still blowing after rescue got there, it must have been 2-4 hours minimum. Oh, well, what's a little frostbite?