Off Road
In the mid 90's I went to the Green Sands Beach in a Land Cruiser, and while there a stock Ford Explorer got stuck while on the trail behind us. We had to pull him and inspect the car for damage before he turned around and went back. Unless the trail is better, I wouldn't try it in my E. I'll be going there later this month or early Feb, depending on the weather, so I'll update and send pix if the trail is easier.
On a more happy note, I did go to the Mauna Kea summit twice this month, once before the snow and once after it snowed. The road can be rough at times, but nothing that really challenges the ground clearance. Of note, I rolled the window down to take a picture and the wonderful aroma of burning break pads filled the E. It was about 55 deg F at the time, so I stopped to let them cool down, drove down about 1,000 more feet then stopped again and let them cool down again. I believe the thin air reduces the ability for air to cool the breaks, plus riding them down for 3,000ft makes a difference too.
I have 3 pictures following of a trip before the most recent snow, and the rest are after. The last one is a Big Island tradition. Most folks with pickup trucks will pile snow as high as they can in the bed and drive home and dump it into the lawn and let the neighborhood kids play in it until it melts. With the E, I was only able to fill a cooler up =( .