We have done this drive along with staying at the Edelweiss Hutte at the top as well. Our weather in mid-June 2011 was not so great. We got snowed in at the top and could see nothing. We had to wait until about noon the next day to leave. Even the folks in the serious 4WD started down and decided it was too icy to leave the parking lot.
Finally someone came up to open the shop in the parking lot and said it was okay, just to go slow. So we did. It was several switchbacks and at least 1000 feet down before we got below the clouds and started seeing less snow. The road was still wet, but not icy at that point. White knuckles all the way for me. There are no guardrails.
If the weather has been good this year, and it is not raining at the bottom when you start up, it should be fine for you. It was raining at the bottom for us, and even though the person who took our money said it should be okay, by the time we got to the top, the rain was much heavier and the wind was blowing sideways.
What we saw on the way up and down before we got into and after we got out of the clouds was beautiful and well worth the drive, but I sure did want to wake up in the morning and see everything from the top. I guess it just wasn't meant to be.