In my youth, my family had a small hobby farm. A daily early morning chore in the winter was feeding the cows. My father would load up the 4X4 with bales and take them out to a feeding area in the field.
One winter morning, after several days of temperatures fluctuating above and below freezing, he "lucked into" getting the 4X4 up onto the snow crust. He had a great time driving around this broad expanse of ice-topped snow, slipping, sliding and spinning up and down the hills of the field. Inevitably, there was a weak spot and the 4X4 crashed through the crust into deep powder - it couldn't get back up on the crust and the powder was too deep to get the traction to push through it. Of course it was a few thousand feet from the farmyard or any trail through the snow. I got corralled into helping retrieve the 4X4.
We pulled out the MF135, only 2WD but chain equipped, and used it like a mini ice-breaker by driving it backwards through the field. About half-way, it bogged down in a spot where the powder was too deep. It had created a trail through the crusted snow but didn't clear a path, so it was truly stuck and couldn't go backwards or forwards.
Next up was the Bobcat skid-steer with a bucket. We used it to remove the snow from the trail the MF135 had made. On a side-slope area, it didn't have the traction to stay in the path and kept sliding sideways. We then decided to have the Bobcat clear a new trail down the slope and around the base so it could stay off any slide slopes. That failed pretty quickly as it got wedged into the snow at a bad angle and wasn't going anywhere.
We were out of equipment - which was just as well as having 3 scattered around the field was enough - so we pulled out the shovels, planks and hay and went to work the old-fashioned way.
It took all day and it was getting pretty dark at the end, but we did get all 3 out.
I've never experienced a snow-crust strong enough to carry a vehicle in the subsequent 35 years - probably a good thing.