I did the Coq run a couple of weeks ago in my Volkswagen Jetta. Mostly night driving, big storm through the passes, and took about 15 hours to complete the journey. I think that an X5 with good tires (M+S) will be just fine.
Here's the catch though - accidents and heavy snow WILL shut down portions of the road. Sometimes these are 30 minute waits, sometimes they are overnight. On my last trip, I had 2 long delays.
If you're in a hurry, ship the vehicle. If you're in a position to 'just roll with it' and can spend a day, two, three.....go for it, it's a great drive.
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