2024 BMW X4

We had snow this afternoon and my wife drove the car home from work. We live on a private road and have a steep driveway. I had her park the car in the road while I plowed the driveway. There was only 1-2” of snow on the ground. My wife existed the car. It appeared to be off and in park meaning the engine was not running and the car sat still on a grade. In hindsight, I should have had her set the park brake. My wife went down to her house taking her key with her. I was plowing the driveway. The car had been sitting still on the road for at least 15 minutes. When I was plowing, I had the other key in my pocket. When I got next to the car while still operating my plow, I noticed the taillights came on. Next, the car began rolling down the hill on its own. Nobody was in the car. I was chasing the car. I noted the rear tires were rolling. They were not sliding. The car contained to roll forward then veered towards the side of the road that has a steep ditch. The car then slide sideways down the embankment and stopped at the bottom of the hill. Fortunately, the car did not rollover. Had it been dry and now snow, I think it would have rolled over sideways due to the steep pitch but instead it slid in the snow. I think I was lucky and there is no significant damage but I have not fully retrieved the car out of the ditch yet. I suspect the car was in the start stop mode and possibly my wife did not put into park before exiting the car but this could be easily done since it has the push buttons shifter and the engine was off. Not sure if this is what happened, it’s just speculation. This could have been much more serious if this happened with other people or cars around.