Same thing happened to PGA golfer Payne Stewart's Lear Jet in 1999. It left Orlando, FL headed for Dallas. They lost cabin pressure and all the passengers and pilot died. The plane kept flying on auto-pilot, ran out of fuel and crashed in South Dakota. They scrambled several fighters over the course of the flight to try and see what was going on. The fighter pilot reported the windows were iced over. You can do a search of the crash site photos and basically it's just a hole in the ground. these are small planes compared to an airliner so when they go down nose first they don't leave a large footprint.

https://en.wikipedia.org/wiki/1999_South_Dakota_Learjet_crash